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Despite substantial progress, the full potential of these methods often remains untapped due to challenges associated with training large supervised models, particularly in the presence of small and class-unbalanced labelled datasets.Self-supervised learning has recently established itself as a powerful methodology to deal with some of the aforementioned challenges, by directly learning a lower-dimensional representation from large samples of unlabelled data. The resulting model and data representation can then be used for data inspection and various downstream tasks if a small subset of labelled data is available.In this work, we explored contrastive learning methods to learn suitable radio data representations by training the SimCLR model on large collections of unlabelled radio images taken from the ASKAP EMU and SARAO MeerKAT GPS surveys. 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data-v-3692cf84><span data-v-63dfaf6e>Publications of the Astronomical Society of Australia</span> </a></li><li class="page-breadcrumbs__item" data-v-3692cf84><span aria-hidden="true" class="breadcrumbs-wrapper__arrow" data-v-3692cf84>></span><a href="/core/journals/publications-of-the-astronomical-society-of-australia/volume/41F60CAF610317F3B352E354D356E178" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-3692cf84><span data-v-63dfaf6e>Volume 41</span> </a></li><li class="page-breadcrumbs__item" data-v-3692cf84><span aria-hidden="true" class="breadcrumbs-wrapper__arrow" data-v-3692cf84>></span><span data-v-3692cf84>Self-supervised contrastive learning of radio data...</span></li></ul></div></div> <div class="language" data-v-3692cf84><ul class="language-switch" data-v-6b1118dd data-v-3692cf84><li aria-label="English" data-v-6b1118dd><span class="language-option current divider" data-v-6b1118dd>English</span></li><li aria-label="Français" data-v-6b1118dd><span role="button" tabindex="0" href="#" lang="fr" class="language-option" data-v-6b1118dd> Français </span></li></ul></div></div></div></div> <div class="container container__modified" data-v-01274b1d>  <div class="row" data-v-01274b1d><div role="complementary" aria-label="table of content" class="column__left" data-v-01274b1d><div class="col journal-container row" data-v-146270e8 data-v-01274b1d><img src="https://static.cambridge.org/covers/PAS_0_0_0/publications-of-the-astronomical-society-of-australia.jpg" alt="" class="journal__image" data-v-146270e8> <a href="/core/journals/publications-of-the-astronomical-society-of-australia" class="app-link journal__title app-link__text app-link--underlined" data-v-63dfaf6e data-v-146270e8><span class="text" data-v-63dfaf6e>Publications of the Astronomical Society of Australia </span> </a> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-146270e8></div>  <div id="toc" class="table-of-content" data-v-01274b1d><h2>Article contents</h2> <div id="toc-list-wrapper" class="table-of-content__wrapper"><ul id="toc-list" class="list"><li class="list__item"><a href="#sec0" class="list__item__link"><span class="toc-title">Abstract</span></a></li> <li class="list__item"><a href="#s1" class="list__item__link"> <span><div class="toc-title">Introduction</div></span></a></li><li class="list__item"><a href="#s2" class="list__item__link"> <span><div class="toc-title">Self-supervised learning of radio data</div></span></a></li><li class="list__item"><a href="#s3" class="list__item__link"> <span><div class="toc-title">Task I: Classification of radio source morphology</div></span></a></li><li class="list__item"><a href="#s4" class="list__item__link"> <span><div class="toc-title">Task II: Radio source detection</div></span></a></li><li class="list__item"><a href="#s5" class="list__item__link"> <span><div class="toc-title">Task III: Search for peculiar objects</div></span></a></li><li class="list__item"><a href="#s6" class="list__item__link"> <span><div class="toc-title">Summary</div></span></a></li><li class="list__item"><a href="#s50" class="list__item__link"> <span><div class="toc-title">Funding statement</div></span></a></li><li class="list__item"><a href="#s51" class="list__item__link"> <span><div class="toc-title">Competing interests</div></span></a></li><li class="list__item"><a href="#s52" class="list__item__link"> <span><div class="toc-title">Data availability statement</div></span></a></li> <li class="list__item"><a href="#footnotes-list" class="list__item__link"><span class="toc-title">Footnotes</span></a></li> <li class="list__item"><a href="#references-list" class="list__item__link"><span class="toc-title">References</span></a></li></ul></div></div></div> <div class="column__main" data-v-01274b1d><div class="row" data-v-01274b1d><div class="column__main__left" data-v-01274b1d><div id="maincontent" class="col" data-v-862424e6 data-v-01274b1d> <hgroup data-v-862424e6><h1 data-v-862424e6>Self-supervised contrastive learning of radio data for source detection, classification and peculiar object discovery</h1> </hgroup>     <div class="row published-date" data-v-862424e6><p data-v-862424e6> Published online by Cambridge University Press: <strong data-v-862424e6>05 November 2024</strong></p></div>   <div class="contributors-details" data-v-99f6eb26 data-v-862424e6><div class="row contributors" data-v-99f6eb26><div class="col" data-v-99f6eb26><div class="row contributor-type" data-v-792406ce data-v-99f6eb26> <div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=S.%20Riggi&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>S. Riggi</span> </a> <a target="_blank" href="https://orcid.org/0000-0001-6368-8330" data-test-orcid="S. Riggi" class="app-link contributor-type__contributor__orcid app-link__icon app-link--" data-v-63dfaf6e data-v-792406ce><img src="data:image/svg+xml;base64,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" alt="Open the ORCID record for S. Riggi" class="app-icon icon orcid" data-v-d2c09870 data-v-63dfaf6e> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a> <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=T.%20Cecconello&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>T. Cecconello</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=S.%20Palazzo&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>S. Palazzo</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=A.M.%20Hopkins&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>A.M. Hopkins</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=N.%20Gupta&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>N. Gupta</span> </a> <a target="_blank" href="https://orcid.org/0000-0001-7652-9451" data-test-orcid="N. Gupta" class="app-link contributor-type__contributor__orcid app-link__icon app-link--" data-v-63dfaf6e data-v-792406ce><img src="data:image/svg+xml;base64,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" alt="Open the ORCID record for N. Gupta" class="app-icon icon orcid" data-v-d2c09870 data-v-63dfaf6e> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a> <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=C.%20Bordiu&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>C. Bordiu</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=A.%20Ingallinera&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>A. Ingallinera</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=C.%20Buemi&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>C. Buemi</span> </a>  <span data-v-792406ce>,</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=F.%20Bufano&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>F. Bufano</span> </a>  <span data-v-792406ce> and</span></div><div class="contributor-type__contributor" data-v-792406ce><a href="/core/search?filters%5BauthorTerms%5D=F.%20Cavallaro&eventCode=SE-AU" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-792406ce><span data-v-63dfaf6e>F. Cavallaro</span> </a>  <span data-v-792406ce></span></div> <a href="#" class="app-link app-link__text-icon app-link--secondary reverse" data-v-63dfaf6e data-v-792406ce><img src="data:image/svg+xml;base64,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" alt="" class="app-icon icon arrow-down" data-v-d2c09870 data-v-63dfaf6e><span class="text" data-v-63dfaf6e>...Show all authors </span> </a></div> </div> <div class="col-2 collapse-link" data-v-99f6eb26><a href="#authors-details" data-toggle="collapse" aria-expanded="false" aria-controls="authors-details" class="app-link collapsed app-link__text-icon app-link--secondary reverse" data-v-63dfaf6e data-v-99f6eb26><img src="data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMTEiIGhlaWdodD0iNiIgdmlld0JveD0iMCAwIDExIDYiIGZpbGw9Im5vbmUiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyI+CjxwYXRoIGZpbGwtcnVsZT0iZXZlbm9kZCIgY2xpcC1ydWxlPSJldmVub2RkIiBkPSJNNS41MDAwNiA2QzUuMzI4NDYgNiA1LjE2Mzk4IDUuOTMzMzkgNS4wNDI1MiA1LjgxNTAxTDAuMTg5NDQ4IDEuMDc3OEMtMC4wNjMxNzYzIDAuODMxMjU3IC0wLjA2MzE3NjMgMC40MzE0NTIgMC4xODk2MSAwLjE4NDkwOEMwLjQ0MjM5NiAtMC4wNjE2MzYgMC44NTIwNjIgLTAuMDYxNjM2IDEuMTA0NTIgMC4xODQ5MDhMNS41MDAwNiA0LjQ3NTc1TDkuODk1NiAwLjE4NDkwOEMxMC4xNDgyIC0wLjA2MTYzNiAxMC41NTc5IC0wLjA2MTYzNiAxMC44MTA1IDAuMTg0OTA4QzExLjA2MzEgMC40MzE0NTIgMTEuMDYzMSAwLjgzMTEgMTAuODEwNyAxLjA3NzhMNS45NTc2IDUuODE1MDFDNS44MzYxNCA1LjkzMzM5IDUuNjcxNjYgNiA1LjUwMDA2IDZaIiBmaWxsPSIjNzA3MDcwIi8+Cjwvc3ZnPgo=" alt="" class="app-icon icon arrow-down" data-v-d2c09870 data-v-63dfaf6e><span class="text" data-v-63dfaf6e>Show author details </span> </a></div></div> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-99f6eb26> <dl id="authors-details" class="authors-details collapse" data-v-2edb8da6 data-v-99f6eb26><div data-test-author="S. Riggi" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>S. Riggi*</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="T. Cecconello" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>T. Cecconello</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span><span data-v-2edb8da6><span data-v-2edb8da6>Department of Electrical, Electronic and Computer Engineering, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy</span> </span></div></dd></div><div data-test-author="S. Palazzo" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>S. Palazzo</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Department of Electrical, Electronic and Computer Engineering, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy</span> </span></div></dd></div><div data-test-author="A.M. Hopkins" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>A.M. Hopkins</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>School of Mathematical and Physical Sciences, 12 Wally’s Walk, Macquarie University, NSW 2109, Australia</span> </span></div></dd></div><div data-test-author="N. Gupta" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>N. Gupta</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>CSIRO Space & Astronomy, PO Box 1130, Bentley WA 6102, Australia</span> </span></div></dd></div><div data-test-author="C. Bordiu" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>C. Bordiu</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="A. Ingallinera" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>A. Ingallinera</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="C. Buemi" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>C. Buemi</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="F. Bufano" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>F. Bufano</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="F. Cavallaro" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>F. Cavallaro</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="M.D. Filipović" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>M.D. Filipović</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>Western Sydney University, Locked Bag 1797, Penrith South DC, NSW 2751, Australia</span> </span></div></dd></div><div data-test-author="P. Leto" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>P. Leto</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="S. Loru" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>S. Loru</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="A.C. Ruggeri" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>A.C. Ruggeri</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="C. Trigilio" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>C. Trigilio</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="G. Umana" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>G. Umana</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div><div data-test-author="F. Vitello" class="row author" data-v-2edb8da6><dt class="col-12 col-sm-2 title" data-v-2edb8da6>F. Vitello</dt> <dd class="col content d-inline d-sm-flex" data-v-2edb8da6><span class="content__title" data-v-2edb8da6>Affiliation:</span> <div class="d-sm-flex flex-column flex-sm-1 d-inline" data-v-2edb8da6><span data-v-2edb8da6><span data-v-2edb8da6>INAF – Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, Italy</span> </span></div></dd></div> <div class="row" data-v-2edb8da6><dt class="col-sm-2 col-12 title" data-v-2edb8da6> * </dt> <dd class="col content" data-v-2edb8da6><div class="row" data-v-2edb8da6><div class="d-sm-flex d-inline flex-sm-1 flex-sm-wrap" data-v-2edb8da6><div class="d-inline" data-v-2edb8da6><span data-v-2edb8da6><div class="corresp"><span class="bold">Corresponding author:</span> S. Riggi; Email: <a href="mailto:simone.riggi@gmail.com">simone.riggi@gmail.com</a>.</div></span></div></div></div></dd></div> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-2edb8da6></dl></div></div> <div id="app-tabs" class="tabs" data-v-1d90c6ce data-v-01274b1d><div id="app-tabs-wrapper" class="tabs__wrapper" data-v-1d90c6ce><div role="navigation" aria-label="tab navigation" class="container" data-v-1d90c6ce><a data-toggle="collapse" href="#appTabs" role="button" aria-expanded="false" aria-controls="appTabs" class="tabs__collapse collapsed d-sm-none d-print-none" data-v-1d90c6ce><span data-v-1d90c6ce></span> <span class="tabs-arrow-up" data-v-1d90c6ce></span> <span class="tabs-arrow-down" data-v-1d90c6ce></span></a> <ul id="appTabs" role="tablist" class="nav nav-tabs tabs__list collapse show" data-v-1d90c6ce><li role="none" class="tabs__tab" data-v-1d90c6ce><a aria-selected="true" href="#article-tab" role="tab" aria-controls="article-tab" tabindex="-1" 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class="toc-title">Abstract</span></a></li> <li class="list__item"><a href="#s1" class="list__item__link"> <span>Introduction</span></a></li><li class="list__item"><a href="#s2" class="list__item__link"> <span>Self-supervised learning of radio data</span></a></li><li class="list__item"><a href="#s3" class="list__item__link"> <span>Task I: Classification of radio source morphology</span></a></li><li class="list__item"><a href="#s4" class="list__item__link"> <span>Task II: Radio source detection</span></a></li><li class="list__item"><a href="#s5" class="list__item__link"> <span>Task III: Search for peculiar objects</span></a></li><li class="list__item"><a href="#s6" class="list__item__link"> <span>Summary</span></a></li><li class="list__item"><a href="#s50" class="list__item__link"> <span>Funding statement</span></a></li><li class="list__item"><a href="#s51" class="list__item__link"> <span>Competing interests</span></a></li><li class="list__item"><a href="#s52" class="list__item__link"> <span>Data availability statement</span></a></li> <li class="list__item"><a href="#footnotes-list" class="list__item__link"><span class="toc-title">Footnotes</span></a></li> <li class="list__item"><a href="#references-list" class="list__item__link"><span class="toc-title">References</span></a></li></ul></div> <div class="action-bar" data-v-43a4d572><div class="row items"> <div class="app-dropdown d-print-none" data-v-fab090b8 data-v-113567da data-v-43a4d572><button aria-expanded="false" data-test-id="buttonSavePDFOptions" id="save-pdf-dropdown" class="app-button dropdown-menu-button app-button__text-icon app-button--secondary" data-v-2a038744 data-v-fab090b8><img src="/core/page-component/img/save-pdf-icon.080470e.svg" alt="" class="app-icon icon save-pdf" data-v-d2c09870 data-v-2a038744> <span class="text" data-v-2a038744>Save PDF</span></button> <div aria-labelledby="save-pdf-dropdown" class="app-dropdown__menu" style="display:none;" data-v-fab090b8><div class="pdf-buttons" 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target="_blank" href="https://s100.copyright.com/AppDispatchServlet?publisherName=CUP&publication=PAS&title=Self-supervised%20contrastive%20learning%20of%20radio%20data%20for%20source%20detection%2C%20classification%20and%20peculiar%20object%20discovery&publicationDate=05%20November%202024&author=S.%20Riggi%2C%20T.%20Cecconello%2C%20S.%20Palazzo%2C%20A.M.%20Hopkins%2C%20N.%20Gupta%2C%20C.%20Bordiu%2C%20A.%20Ingallinera%2C%20C.%20Buemi%2C%20F.%20Bufano%2C%20F.%20Cavallaro%2C%20M.D.%20Filipovi%C4%87%2C%20P.%20Leto%2C%20S.%20Loru%2C%20A.C.%20Ruggeri%2C%20C.%20Trigilio%2C%20G.%20Umana%2C%20F.%20Vitello©right=%C2%A9%20The%20Author(s)%2C%202024.%20Published%20by%20Cambridge%20University%20Press%20on%20behalf%20of%20Astronomical%20Society%20of%20Australia&contentID=10.1017%2Fpasa.2024.84&startPage=&endPage=&orderBeanReset=True&volumeNum=41&issueNum=&oa=" data-test-id="buttonRightLink" class="app-link rights-link d-print-none app-link__text-icon app-link--accent" data-v-63dfaf6e data-v-92ee52a2 data-v-43a4d572><img src="/core/page-component/img/rights-icon.d4a677c.svg" alt="" class="app-icon icon rights" data-v-d2c09870 data-v-63dfaf6e><span class="text" data-v-63dfaf6e>Rights & Permissions </span> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a></div> <hr aria-hidden="true" class="separator default" data-v-7036083a></div> <div class="share-modal-overlay" style="display:none;" data-v-43a4d572></div> <div data-spy="scroll" data-target="#toc" class="scrollspy-content" data-v-43a4d572> <div id="sec0" class="col article-abstract sec" data-v-2fa8b348 data-v-43a4d572><div class="abstract-text-container" data-v-2fa8b348><div lang="en"><h2>Abstract</h2>  <div class="abstract-content"><div class="abstract" data-abstract-type="normal"><p>New advancements in radio data post-processing are underway within the Square Kilometre Array (SKA) precursor community, aiming to facilitate the extraction of scientific results from survey images through a semi-automated approach. Several of these developments leverage deep learning methodologies for diverse tasks, including source detection, object or morphology classification, and anomaly detection. Despite substantial progress, the full potential of these methods often remains untapped due to challenges associated with training large supervised models, particularly in the presence of small and class-unbalanced labelled datasets.</p><p>Self-supervised learning has recently established itself as a powerful methodology to deal with some of the aforementioned challenges, by directly learning a lower-dimensional representation from large samples of unlabelled data. The resulting model and data representation can then be used for data inspection and various downstream tasks if a small subset of labelled data is available.</p><p>In this work, we explored contrastive learning methods to learn suitable radio data representations by training the SimCLR model on large collections of unlabelled radio images taken from the ASKAP EMU and SARAO MeerKAT GPS surveys. The resulting models were fine-tuned over smaller labelled datasets, including annotated images from various radio surveys, and evaluated on radio source detection and classification tasks. Additionally, we employed the trained self-supervised models to extract features from radio images, which were used in an unsupervised search for objects with peculiar morphology in the ASKAP EMU pilot survey data. For all considered downstream tasks, we reported the model performance metrics and discussed the benefits brought by self-supervised pre-training, paving the way for building radio foundational models in the SKA era.</p></div></div> <hr aria-hidden="true" class="abstract-divider separator default" data-v-7036083a></div></div>   </div>  <div class="keywords" data-v-86c27100 data-v-43a4d572><h2 data-v-86c27100>Keywords</h2> <div class="row keywords__pills" data-v-86c27100><a href="/core/search?filters[keywords]=Radio sources" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>Radio sources</span></a><a href="/core/search?filters[keywords]=radio source catalogs" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>radio source catalogs</span></a><a href="/core/search?filters[keywords]=astronomy image processing" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>astronomy image processing</span></a><a href="/core/search?filters[keywords]=deep learning" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>deep learning</span></a><a href="/core/search?filters[keywords]=classification" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>classification</span></a><a href="/core/search?filters[keywords]=outlier detection" data-v-f0b31360 data-v-86c27100><span data-v-f0b31360 data-v-86c27100>outlier detection</span></a></div> <hr aria-hidden="true" class="separator default" data-v-7036083a data-v-86c27100></div>  <dl class="article-details" data-v-6e32a161 data-v-43a4d572><div class="row" data-v-6e32a161><dt class="col-12 col-sm-3 col-md-2_5 title" data-v-6e32a161> Type </dt> <dd class="col content" data-v-6e32a161>Research Article</dd></div> <div class="row" data-v-6e32a161><dt class="col-12 col-sm-3 col-md-2_5 title" data-v-6e32a161> Information </dt> <dd class="col content" data-v-6e32a161><div class="content__journal" data-v-6e32a161><a href="/core/journals/publications-of-the-astronomical-society-of-australia" class="app-link app-link__text app-link--underlined" data-v-63dfaf6e data-v-6e32a161><span class="text" data-v-63dfaf6e>Publications of the Astronomical Society of Australia </span> </a> <span data-v-6e32a161> , <a href="/core/journals/publications-of-the-astronomical-society-of-australia/volume/41F60CAF610317F3B352E354D356E178" class="app-link app-link__text app-link--underlined" data-v-63dfaf6e data-v-6e32a161><span class="text" data-v-63dfaf6e>Volume 41 </span> </a></span>  <span data-v-6e32a161>, 2024</span>   <span data-v-6e32a161>, e085</span></div> <div class="doi-data" data-v-6e32a161><div data-v-6e32a161>DOI: <a target="_blank" href="https://doi.org/10.1017/pasa.2024.84" class="app-link app-link__text app-link--accent" data-v-63dfaf6e data-v-6e32a161><span class="text" data-v-63dfaf6e>https://doi.org/10.1017/pasa.2024.84 </span> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a></div> <a data-target="crossmark" aria-label="Check for updates" href="#" class="crossmark-widget" data-v-6e32a161><img src="/core/page-component/img/crossmark-logo.61d5da3.svg" alt="Check for updates" data-v-6e32a161></a></div>  <div data-v-6e32a161><a target="_blank" href="https://ui.adsabs.harvard.edu/abs/10.1017/pasa.2024.84" class="app-link app-link__text app-link--underlined" data-v-63dfaf6e data-v-6e32a161><span class="text" data-v-63dfaf6e>NASA ADS Abstract Service </span> <span class="sr-only" data-v-63dfaf6e>[Opens in a new window]</span></a></div></dd></div>   <div class="row" data-v-6e32a161><dt class="col-12 col-sm-3 col-md-2_5 title" data-v-6e32a161> Copyright </dt> <dd class="col content" data-v-6e32a161><div data-v-6e32a161> © The Author(s), 2024. Published by Cambridge University Press on behalf of Astronomical Society of Australia </div></dd></div></dl>  <div id="content-container" class="content-container" data-v-43a4d572><div class="content-box"><div class="article research-article NLM"> <div class="body"> <div class="sec intro" data-magellan-destination="s1" id="s1"> <h2 class="A"><span class="label">1.</span> Introduction</h2> <p class="p"> Radio astronomy stands at the threshold of a transformative era, marked by the advent of large sky surveys carried out with instruments such as the Square Kilometre Array (SKA) (Dewdney et al., <a class="xref bibr" href="#ref12"><span class="show-for-sr">Reference Dewdney</span>2016</a>) and its precursor telescopes. As the field enters this golden age, the immense volumes of observational data generated pose unprecedented challenges and opportunities. For example, the Evolutionary Map of the Universe (EMU) (Norris et al., <a class="xref bibr" href="#ref40"><span class="show-for-sr">Reference Norris</span>2011</a>) of the Australian SKA Pathfinder (ASKAP, Johnston et al., <a class="xref bibr" href="#ref24"><span class="show-for-sr">Reference Johnston</span>2008</a>; Hotan et al., <a class="xref bibr" href="#ref22"><span class="show-for-sr">Reference Hotan</span>2021</a>) started in 2022 to survey <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline1.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline1.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>75% of the sky at 940 MHz with an angular resolution of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline2.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline2.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>15<sup class="sup">′′</sup> and a noise rms of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline3.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline3.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>15 <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline4.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="11" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline4.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mu$ </span></span> </span> </span>Jy/beam. The EMU source cataloguing process will require an unprecedented degree of automation and knowledge extraction, as the expected number of detectable sources is <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline5.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline5.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>50 millions. So will be for other precursors and future SKA observations. The sheer scale and complexity of these datasets demand innovative approaches to shorten the time needed to deliver scientific results or groundbreaking discoveries.</p> <p class="p"> In this context, machine learning (ML) emerges as a powerful tool for unlocking the full potential of radio astronomy data, offering solutions to complex tasks that are often beyond the reach of conventional methods in multiple areas, including source extraction, classification (e.g. morphological or astrophysical type) and discovery of anomalous/unexpected objects. Most existing contributions focused on galaxy morphology classification for extragalactic science cases employing either supervised learning (SL), e.g. with convolutional neural networks (CNNs) (Aniyan & Thorat <a class="xref bibr" href="#ref1"><span class="show-for-sr">Reference Aniyan and Thorat</span>2017</a>; Lukic et al., <a class="xref bibr" href="#ref33"><span class="show-for-sr">Reference Lukic</span>2018</a>; Wu et al., <a class="xref bibr" href="#ref58"><span class="show-for-sr">Reference Wu</span>2019</a>; Lao et al., <a class="xref bibr" href="#ref28"><span class="show-for-sr">Reference Lao</span>2023</a>) or Vision Transformers (ViTs) (Gupta et al., <a class="xref bibr" href="#ref17"><span class="show-for-sr">Reference Gupta</span>2024</a>), weakly-supervised learning (Gupta et al., <a class="xref bibr" href="#ref18"><span class="show-for-sr">Reference Gupta</span>2023</a>), semi-supervised learning (Slijepcevic et al., <a class="xref bibr" href="#ref49"><span class="show-for-sr">Reference Slijepcevic</span>2022</a>), or unsupervised learning, e.g. Self-Organizing Maps (SOMs) (Galvin et al., <a class="xref bibr" href="#ref13"><span class="show-for-sr">Reference Galvin</span>2020</a>; Mostert et al., <a class="xref bibr" href="#ref37"><span class="show-for-sr">Reference Mostert</span>2021</a>; Gupta et al., <a class="xref bibr" href="#ref19"><span class="show-for-sr">Reference Gupta</span>2022</a>) or t-distributed stochastic neighbour embedding (Pennock et al., <a class="xref bibr" href="#ref43"><span class="show-for-sr">Reference Pennock</span>2022</a>).</p> <p class="p"> Despite substantial progress, the full potential of supervised approaches often remains untapped due to the scarcity of large and high-quality annotated radio image datasets, crucial for training very deep models. The human effort required to produce them is in fact unsustainable. Citizen science projects, launched within different precursor surveys on the Zooniverse platform<a class="xref fn" href="#fn1"><span class="show-for-sr">Footnote </span> <sup class="sup">a</sup> </a> <sup class="sup">,</sup> <a class="xref fn" href="#fn2"><span class="show-for-sr">Footnote </span> <sup class="sup">b</sup> </a> and building on the previous Radio Galaxy Zoo project (Banfield et al., <a class="xref bibr" href="#ref2"><span class="show-for-sr">Reference Banfield</span>2015</a>), will partially alleviate this need, at the cost of potentially introducing errors and biases in the cumulative dataset. As a result, existing labelled radio datasets are typically very limited in size, class-unbalanced, and adopt a diverse or ambiguous labelling schema, usually depending on the particular domain of application. Several applications produced so far for either radio source classification or source detection scopes, have therefore resorted to fine-tune models that were previously pre-trained on large annotated collections of non-astronomical data, such as the <em class="italic">ImageNet</em> (Deng et al., <a class="xref bibr" href="#ref11"><span class="show-for-sr">Reference Deng</span>2009</a>) or <em class="italic">COCO</em> (Tsung-Yi et al., <a class="xref bibr" href="#ref53"><span class="show-for-sr">Reference Tsung-Yi</span>2014</a>) datasets, that may not well capture all distinctive features of radio observations. On the other hand, completely unsupervised approaches are not very effective when directly dealing with highly dimensional image data, typically requiring previous feature extraction and dimensionality reduction steps to be applied. Currently, employed methods based on SOMs typically enforce an apriori discrete static data organization that do not well support extension to new tasks. These limitations necessitate exploring alternative methodologies.</p> <p class="p"> Representation learning (Bengio & Anal <a class="xref bibr" href="#ref4"><span class="show-for-sr">Reference Bengio and Anal</span>2013</a>), and in particular self-supervised learning (SSL) (Liu et al., <a class="xref bibr" href="#ref32"><span class="show-for-sr">Reference Liu</span>2023</a>), has recently emerged as a promising avenue to address these issues, by directly learning (pretext task), without any supervision, a lower-dimensionality representation (i.e. the latent space) from large samples of unlabelled data. The resulting model and data representation can then be used for data inspection and generalized for various applications (downstream tasks), e.g. classification, object detection, etc, if a small subset of labelled data is available. Previous works in the radio domain are based on convolutional autoencoders (CAE) generative methods, which learns a latent space by minimizing a loss between input data and data reconstructed through an encoder-decoder network. For example, Ralph et al. <a class="xref bibr" href="#ref45"><span class="show-for-sr">Reference Ralph</span>2019</a> developed a pipeline for unsupervised source morphology studies based on SOMs and k-mean clustering algorithm, employing CAEs to extract features from the Radio Galaxy Zoo (RGZ) (Banfield et al., <a class="xref bibr" href="#ref2"><span class="show-for-sr">Reference Banfield</span>2015</a>) images. Bordiu et al. (<a class="xref bibr" href="#ref7"><span class="show-for-sr">Reference Bordiu</span>2023</a>) employed CAEs to extract features from combined radio and infrared images of known Galactic supernova remnants (SNRs) to search for possible multiwavelength patterns.</p> <p class="p"> Contrastive learning approaches, on the other hand, employ siamese or teacher-student network architectures, minimizing the similarity between augmented versions of the input data, eventually in contrast to negative samples. They were reported to obtain superior performance on natural images in classification tasks (e.g. rivalling supervised methods), quality of representation learnt, computation efficiency, and robustness to noise. Recently, Slijepcevic et al. (<a class="xref bibr" href="#ref50"><span class="show-for-sr">Reference Slijepcevic</span>2024</a>) trained BYOL (Grill et al., <a class="xref bibr" href="#ref15"><span class="show-for-sr">Reference Grill</span>2020</a>) contrastive learning method over a sample of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline6.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline6.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>10<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline7.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="5" height="7" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline7.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $^{5}$ </span></span> </span> </span> radio source RGZ images from the VLA FIRST survey (Becker et al., <a class="xref bibr" href="#ref3"><span class="show-for-sr">Reference Becker</span>1995</a>). The resulting self-supervised model was then fine-tuned to classify FRI/FRII radio galaxies from the VLA FIRST survey, as listed in the <em class="italic">Mirabest</em> dataset (Porter & Scaife <a class="xref bibr" href="#ref44"><span class="show-for-sr">Reference Porter and Scaife</span>2023</a>). The analysis was repeated over a second dataset that include data from the MeerKAT MIGHTEE survey. Both analyses indicated an increase in classification accuracy (ranging from few percent to 8% for MIGHTEE) over the same model trained in a completely supervised way. Mohale & Lochner (<a class="xref bibr" href="#ref36"><span class="show-for-sr">Reference Mohale and Lochner</span>2024</a>) carried out a similar FRI/FRII classification analysis over the <em class="italic">Mirabest</em> dataset, using self-supervised models, previously pre-trained over the <em class="italic">ImageNet-1k</em> (natural images), RGZ (radio galaxy images), Galaxy Zoo DECaLS (optical galaxy images) datasets. Using a KNN classifier evaluation, they found that the model pre-trained on RGZ outperforms the others by a considerable margin (5% to 10% improvement in accuracy). Hossain et al. (<a class="xref bibr" href="#ref21"><span class="show-for-sr">Reference Hossain</span>2023</a>) carried out the same analysis with both BYOL and SimCLR (Chen et al., 2020) self-supervised models but using Group Equivariant Convolutional Neural Network (G-CNN) backbones to make models invariant to different isometries (translation, rotation, mirror reflection). They pre-trained self-supervised models on the RGZ dataset and fine-tuned them on <em class="italic">Mirabest</em> dataset, obtaining FRI/FRII classification accuracies around 95%-97%<a class="xref fn" href="#fn3"><span class="show-for-sr">Footnote </span> <sup class="sup">c</sup> </a>, improving by <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline8.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline8.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>2% the fully supervised baseline.</p> <p class="p"> With respect to previous studies, we focused more on SKA precursor data, training the SimCLR self-supervised model over large samples of unlabelled images, extracted from ASKAP and MeerKAT radio maps in two different modes: (1) “source-centered” mode, e.g. images centred and zoomed over catalogued sources (as in previous studies); (2) “blind” or “random” mode, e.g. images with arbitrary fixed size extracted from the entire map, without any source position awareness. The backbone component of the trained self-supervised models, a <em class="italic">ResNet18</em> neural network, was then evaluated and fine-tuned on labelled datasets to solve two representative radio source analysis tasks: radio source morphology classification and radio source instance segmentation. Additionally, the backbone model was used as a feature extractor for radio images, enabling an unsupervised search for radio objects with peculiar morphology based on the extracted data representation. Compared to previous studies, we assessed the trained models over larger labelled datasets, comprising thousands of annotated images from various radio surveys (VLA FIRST, ASKAP pilot, ATCA Scorpio), that were not previously used for self-supervised model pre-training. This study aims to quantify the benefits of self-supervision for the radio domain, providing ready-to-use foundational models that can be exploited in SKA precursor or other radio surveys as feature extractors for similar analysis or to tackle completely new tasks.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f1" id="f1"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig1.png?pub-status=live" class="aop-lazy-load-image" width="5177" height="2445" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig1.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 1.</span> Schema of self-supervised learning for radio data analysis.</p> </div></div></section> <p class="p"> The paper is organized as follows. In <a class="xref sec" href="#s2">Section 2</a> we describe the contrastive learning model considered, along with the training datasets, data pre-processing and training methodologies adopted. In <a class="xref sec" href="#s3">Sections 3</a>, <a class="xref sec" href="#s4">4</a>, and <a class="xref sec" href="#s5">5</a> we studied how the trained self-supervised models perform in the three selected analysis scenarios, reporting performances achieved against benchmark supervised models. Finally, in <a class="xref sec" href="#s6">Section 6</a> we summarize the obtained results and discuss future steps.</p> </div> <div class="sec other" data-magellan-destination="s2" id="s2"> <h2 class="A"><span class="label">2.</span> Self-supervised learning of radio data</h2> <div class="sec" data-magellan-destination="s2-1" id="s2-1"> <h3 class="B"><span class="label">2.1</span> Contrastive learning model</h3> <p class="p"> <a class="xref fig" href="#f1">Figure 1</a> illustrates how self-supervised learning can be used for radio data analysis. Initially, a self-supervised framework (indicated by the red block) is trained on large samples of unlabelled image data. Subsequently, the resulting model backbone and data representation (or latent space vector) can be utilized for various downstream tasks, such as data inspection or anomaly detection, typically employing dimensionality reduction methods. Furthermore, the model can be applied to source detection and classification analysis using new labelled datasets. In this study, we used <em class="italic">SimCLR</em> as the self-supervised framework for our analysis.</p> <p class="p"> SimCLR (Chen et al., 2020) is a simple yet widely used popular self-supervised learning framework. It learns data representations by maximizing the similarity between augmented views of the same input data (<em class="italic">positive examples</em>) relative to augmented views of different input data within the same training batch (<em class="italic">negative examples</em>). The architecture of SimCLR, depicted in <a class="xref fig" href="#f1">Figure 1</a>, consists of two main components: a base encoder network <em class="italic">f</em>, which is typically a <em class="italic">ResNet</em> network (He et al., <a class="xref bibr" href="#ref20"><span class="show-for-sr">Reference He</span>2016</a>), and a small projection head network <em class="italic">g</em>, which is typically a Multi-Layer Perceptron (MLP) with one or two layers. Input images <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline9.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="13" height="9" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline9.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathbf{x}_{k}$ </span></span> </span> </span> (<em class="italic">k</em> = 1,...,N) in a given batch sample of size <em class="italic">N</em> are first processed to produce two augmented views (or positive pair) <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline10.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="30" height="14" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline10.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\hat{\mathbf{x}}_{2k-1}$ </span></span> </span> </span> and <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline11.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="18" height="14" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline11.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\hat{\mathbf{x}}_{2k}$ </span></span> </span> </span>, by randomly applying multiple transformations from a specified transform set <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline12.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="13" height="12" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline12.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathcal{T}$ </span></span> </span> </span>. The encoder network, also denoted as the <em class="italic">backbone model</em> throughout the paper, extracts representation vectors <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline13.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="102" height="16" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline13.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathbf{h}_{2k-1}= f(\mathbf{x}_{2k-1})$ </span></span> </span> </span> and <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline14.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="74" height="16" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline14.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathbf{h}_{2k}= f(\mathbf{x}_{2k})$ </span></span> </span> </span> from each augmented data pair. The projector network maps the representations to a space where a contrastive loss is applied, obtaining vectors <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline15.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="102" height="16" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline15.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathbf{z}_{2k-1}= g(\mathbf{h}_{2k-1})$ </span></span> </span> </span> and <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline16.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="74" height="16" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline16.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathbf{z}_{2k}= g(\mathbf{h}_{2k})$ </span></span> </span> </span>. The contrastive loss <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline17.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="11" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline17.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathcal{L}$ </span></span> </span> </span>, which is minimized during model training, is defined as: </p><div data-mathjax-status="alt-graphic" class="disp-formula" data-magellan-destination="disp1" id="disp1"> <span class="label">(1)</span> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn1.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="192" height="47" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn1.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> \begin{align}\mathcal{L} = \frac{1}{2N}\sum_{k=1}^{N}[l_{2k-1,2k} + l_{2k,2k-1}]\end{align} </span></span> </span> </div> <div data-mathjax-status="alt-graphic" class="disp-formula" data-magellan-destination="disp2" id="disp2"> <span class="label">(2)</span> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn2.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="255" height="42" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn2.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> \begin{align}l_{i,j} = -\log{\frac{\exp\!(\text{sim}(\mathbf{z}_{i},\mathbf{z}_{j})/\tau)}{\sum_{k=1}^{2N} \unicode{x1D7D9}_{k\neq i} \exp\!(\text{sim}(\mathbf{z}_{i},\mathbf{z}_{k})/\tau)}}\end{align} </span></span> </span> </div><p class="p continuation">where <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline18.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="16" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline18.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $l_{i,j}$ </span></span> </span> </span> is the normalized temperature-scaled cross entropy loss (NT-Xent), <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline19.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="27" height="17" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline19.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\unicode{x1D7D9}_{k \neq i}$ </span></span> </span> </span> = 1 if <em class="italic">k</em> = <em class="italic">i</em> (equal to 0 otherwise), <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline20.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="8" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline20.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\tau$ </span></span> </span> </span> is a temperature parameter, and <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline21.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="62" height="17" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline21.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\text{sim}(\mathbf{z}_i,\mathbf{z}_j)$ </span></span> </span> </span> is the pair-wise similarity between vectors <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline22.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="9" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline22.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathbf{z}_i$ </span></span> </span> </span> and <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline23.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="12" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline23.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathbf{z}_j$ </span></span> </span> </span>, defined as: </p><div data-mathjax-status="alt-graphic" class="disp-formula" data-magellan-destination="disp3" id="disp3"> <span class="label">(3)</span> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn3.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="151" height="42" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn3.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> \begin{align}\text{sim}(\mathbf{z}_i,\mathbf{z}_j)= \frac{\mathbf{z}_{i}^{T}\mathbf{z}_j}{\parallel\mathbf{z}_i\parallel\;\parallel\mathbf{z}_j\parallel }\end{align} </span></span> </span> </div> </div> <div class="sec" data-magellan-destination="s2-2" id="s2-2"> <h3 class="B"><span class="label">2.2</span> Datasets</h3> <p class="p"> We created the following unlabelled datasets for training SimCLR:</p><ol class="list number nomark"> <li class="list-item"> <p class="p"><span class="label">1.</span> Two distinct datasets were generated using data from the SARAO MeerKAT Galactic Plane Survey (SMGPS) (Goedhart et al., <a class="xref bibr" href="#ref14"><span class="show-for-sr">Reference Goedhart</span>2024</a>), which covers a large portion of the 1st, 3rd and 4th Galactic quadrants (l = 2<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline24.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="5" height="5" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline24.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $^{\circ}$ </span></span> </span> </span>−61<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline25.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="5" height="5" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline25.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $^{\circ}$ </span></span> </span> </span>, 251<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline26.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="5" height="5" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline26.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $^{\circ}$ </span></span> </span> </span>−358<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline27.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="5" height="5" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline27.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $^{\circ}$ </span></span> </span> </span>, <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline28.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="29" height="14" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline28.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $|b| \lt $ </span></span> </span> </span>1.5<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline29.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="5" height="5" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline29.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $^{\circ}$ </span></span> </span> </span>) in the L-band (886–1 678 MHz). The survey has an angular resolution of 8<sup class="sup">′′</sup> and a noise rms of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline30.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline30.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>10-20 <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline31.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="11" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline31.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mu$ </span></span> </span> </span>Jy/beam at 1.3 GHz:<ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">hulk_smgps</span>: A collection of 178,057 radio images, each of fixed size (256<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline32.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline32.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span>256 pixels, equivalent to <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline33.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline33.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>6.4’<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline34.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline34.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span>6.4’), extracted from SMGPS 1.28 GHz integrated intensity maps. This dataset was created by assuming a sliding window that traverses the entire surveyed area with a shift size equal to half the frame size, resulting in a 50% overlap among frames. The image size was chosen to be large enough to encompass the most extended radio galaxies that might be located in the cutout<a class="xref fn" href="#fn4"><span class="show-for-sr">Footnote </span> <sup class="sup">d</sup> </a>;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">banner_smgps</span>: A collection of 17 062 radio images extracted from SMGPS 1.3 GHz integrated maps, each centered around sources listed in the SMGPS extended source catalogue (Bordiu et al., <a class="xref bibr" href="#ref6"><span class="show-for-sr">Reference Bordiu</span>2024</a>). The size of the images varies across the dataset and is set to 1.5 times the size of the source bounding box. The radio sources in this dataset exhibit different morphologies, including single-island, multi-island, and diffuse sources.</p> </li> </ul> </p> </li> <li class="list-item"> <p class="p"><span class="label">2.</span> Two distinct datasets were generated using data from the ASKAP EMU pilot survey (Norris et al., <a class="xref bibr" href="#ref41"><span class="show-for-sr">Reference Norris</span>2021</a>a), which covered approximately 270 deg<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline36.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="5" height="7" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline36.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $^{2}$ </span></span> </span> </span> of the Dark Energy Survey area, achieving an angular resolution of 11<sup class="sup">′′</sup> to 18<sup class="sup">′′</sup> and a noise rms of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline37.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline37.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>30 <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline38.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="11" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline38.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mu$ </span></span> </span> </span>Jy/beam at 944 MHz:<ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">hulk_emupilot</span>: A collection of 55 773 radio images, each of fixed size (256<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline39.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline39.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span>256 pixels, equivalent to <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline40.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline40.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>8.5’<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline41.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline41.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span>8.5’), extracted from ASKAP EMU pilot 944 MHz integrated map. The images were extracted using a sliding frame that traversed the entire mosaic with a shift size equal to half the frame size, resulting in a 50% overlap among frames.</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">banner_emupilot</span>: A collection of 10,414 radio images extracted from ASKAP EMU pilot 944 MHz integrated map, each centered around extended sources listed in the pilot source catalogue compiled by Gupta et al. (<a class="xref bibr" href="#ref17"><span class="show-for-sr">Reference Gupta</span>2024</a>). The size of the images varies across the dataset and is set to 1.5 times the size of the source bounding box. The radio sources in this dataset exhibit different morphologies, including FR-I (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline42.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline42.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>6%), FR-II (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline43.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline43.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>54%), FR-x (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline44.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline44.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>14%), single-peak resolved (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline45.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline45.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>23%) radio galaxies. <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline46.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline46.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>3% of the sources present a rare morphology not fitting into the previously mentioned categories.</p> </li> </ul> </p> </li> </ol> <p class="p"> Datasets extracted in a blind mode (e.g. without any previous knowledge of the source location and morphology) can be constructed rapidly, potentially reaching substantial sizes (up to millions of images) when using future full-sky surveys. Without additional selection processes, these datasets tend to be largely unbalanced, predominantly comprising frames composed entirely of compact sources. The <span class="monospace">hulk_smgps</span> dataset also comprises frames with large-scale diffuse emission, including background or portions of very extended sources located along the Galactic plane. For simplicity, we have labelled them as <span class="monospace">hulk</span>. In contrast, “smarter” datasets centered on selected source positions typically have smaller sizes, requiring significant efforts (catalogue production and source type annotation) for construction. We have labelled them as <span class="monospace">banner</span>. Indeed, one goal of this work is evaluating differences and benefits of both kind of datasets over different analysis tasks. Summary information for all produced datasets is reported in <a class="xref table" href="#tbl1">Table 1</a>. In <a class="xref fig" href="#f2">Figure 2</a> we display sample images from the <span class="monospace">hulk_smgps</span> (top panels), <span class="monospace">banner_smgps</span> (middle panels) and <span class="monospace">banner_emupilot</span> (bottom panels) datasets.</p> <p class="p"> </p><div class="table-wrap" data-magellan-destination="tbl1" id="tbl1"> <div class="caption"> <p class="p"><span class="label">Table 1.</span> Summary information of datasets used for SimCLR model training. The number of images <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline47.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="25" height="12" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline47.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $n_{img}$ </span></span> </span> </span> is reported in column (2). The image size <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline48.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="22" height="12" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline48.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $s_{img}$ </span></span> </span> </span> is reported in column (3). <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline49.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="22" height="12" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline49.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $s_{img}$ </span></span> </span> </span> is fixed for all images in the <span class="monospace">hulk_smgp</span> and <span class="monospace">hulk_emupilot</span> datasets, while <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline50.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="22" height="12" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline50.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $s_{img}$ </span></span> </span> </span> is not fixed and depends on the source size <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline51.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="35" height="9" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline51.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $s_{\text{source}}$ </span></span> </span> </span> (equivalent to the maximum source bounding box dimension) in the <span class="monospace">banner_smgps</span> and <span class="monospace">banner_emupilot</span> datasets. For these datasets, we report the average, minimum and maximum source sizes in columns (4), (5) and (6), respectively. Images from all datasets are eventually resized to a fixed size for model training and testing (see <a class="xref sec" href="#s2-3">Section 2.3</a>).</p> </div> <span> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab1.png?pub-status=live" class="aop-lazy-load-image" width="399" height="155" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab1.png" data-zoomable="false"></div> </span> </div> <p class="p"> </p><section><div class="fig" data-magellan-destination="f2" id="f2"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig2.png?pub-status=live" class="aop-lazy-load-image" width="5187" height="5154" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig2.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 2.</span> Representative examples of images from the <span class="monospace">hulk_smgps</span> (top panels), <span class="monospace">banner_smgps</span> (middle panels) and <span class="monospace">hulk_emupilot</span> (bottom panels) datasets. A zscale transform was applied to all images for visualization scopes. Top panels: sample images containing only compact sources (<a class="xref fig" href="#f2">Figure 2</a>(a)), or multiple extended sources (<a class="xref fig" href="#f2">Figures 2</a>(b) and <a class="xref fig" href="#f2">2</a>(c)). Middle panels: sample source with diffuse morphology (<a class="xref fig" href="#f2">Figure 2</a>(d)), a multi-component extended source exhibiting typical radio galaxy morphology (<a class="xref fig" href="#f2">Figure 2</a>(e)), a single-component extended source with a roundish morphology (<a class="xref fig" href="#f2">Figure 2</a>(f)). Bottom panels: sample sources with FR-I (<a class="xref fig" href="#f2">Figure 2</a>(g)), FR-II (<a class="xref fig" href="#f2">Figure 2</a>(h)) and peculiar (<a class="xref fig" href="#f2">Figure 2</a>(i)) classification.</p> </div></div></section> </div> <div class="sec" data-magellan-destination="s2-3" id="s2-3"> <h3 class="B"><span class="label">2.3</span> Data pre-processing and augmentation</h3> <p class="p"> For the training and inference stages, we applied these pre-processing steps to input images:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> Grayscale images were converted to 3-channels. Each channel was processed differently from others, applying the following transformations:<ol class="list number nomark"> <li class="list-item"> <p class="p"><span class="label">-</span> <em class="italic">Channel 1</em>: sigma-clipping (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline66.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="24" height="10" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline66.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sigma_{low}$ </span></span> </span> </span> = 5, <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline67.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="19" height="13" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline67.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sigma_{up}$ </span></span> </span> </span> = 30);</p> </li> <li class="list-item"> <p class="p"><span class="label">-</span> <em class="italic">Channel 2</em>: zscale transform (contrast = 0.25);</p> </li> <li class="list-item"> <p class="p"><span class="label">-</span> <em class="italic">Channel 3</em>: zscale transform (contrast = 0.4).</p> </li> </ol> </p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> Each channel was independently normalized to a [0,1] range using a <em class="italic">MinMax</em> transformation;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> Finally, each channel was resized to a 224<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline68.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline68.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span>224 size in pixels.</p> </li> </ul> <p class="p"> A key aspect when training contrastive learning models is the choice of applied data augmentation steps to make the model invariant with respect to non-physical properties or to features not related to the radio sources. We applied the following augmenters to the data sequentially:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">RandomCropResize</em>: randomly crop input images to size <span class="monospace">crop_size</span> <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline69.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline69.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span> image size, and resize data to the original size. <span class="monospace">crop_size</span> was randomly varied in the range [0.8, 1.0];</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">ColorJitter</em>: apply a colour jitter transformation using all three image channels;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">Flip</em>: random flip images either vertically or horizontally;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">Rotate</em>: rotate images by either 90, 180 or 270 degrees;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">Blur</em>: apply Gaussian blurring to images using a <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline70.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline70.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sigma$ </span></span> </span> </span> parameter randomly varied in the range [1,3];</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">RandomThresholding</em>: threshold each channel separately using a per-channel percentile threshold randomly varied in the range [40,60].</p> </li> </ul> <p class="p"> The <em class="italic">RandomThresholding</em> augmenter was introduced to make the model less dependent on image background features. This stage was not applied when training over the <span class="monospace">banner</span> datasets, as images in this dataset are already zoomed on radio sources, and thus the background would likely not be estimated correctly. Furthermore, not all augmenters are applied to every image in the training dataset. In <a class="xref table" href="#tbl2">Table 2</a> we provide a summary of augmenter steps used in the pre-processing pipeline with their parameters, including the probability with which each data transform is applied to images. With respect to Chen et al. (2020), we reduced the fraction of random cropping allowed to avoid cutting out relevant details of extended sources from the resulting image.</p> </div> <div class="sec" data-magellan-destination="s2-4" id="s2-4"> <h3 class="B"><span class="label">2.4</span> Model training</h3> <p class="p"> We trained a SimCLR model on each of the four datasets described in <a class="xref sec" href="#s2-2">Section 2.2</a>, using the hyperparameters listed in <a class="xref table" href="#tbl3">Table 3</a>. We will refer to them using their training dataset name: <span class="monospace">hulk_smgps</span>, <span class="monospace">banner_smgps</span>, <span class="monospace">hulk_emupilot</span>, and <span class="monospace">banner_emupilot</span>. A fourth model, referred to as <span class="monospace">smart_hulk_smgps</span> hereafter, was trained in two steps, first on the <span class="monospace">hulk_smgps</span> dataset and then on the <span class="monospace">banner_smgps</span> dataset. The final model weights from the first step were used as initialization for the second step. For all models, we used a <em class="italic">ResNet18</em> (He et al., <a class="xref bibr" href="#ref20"><span class="show-for-sr">Reference He</span>2016</a>) encoder and a 2-layer projector with 256 and 128 neurons, respectively.</p> <p class="p"> </p><div class="table-wrap" data-magellan-destination="tbl2" id="tbl2"> <div class="caption"> <p class="p"><span class="label">Table 2.</span> List of augmentations used in SimCLR model training. In column (2) we reported the transform parameter values. In column (3) we reported the probability used to apply the transform in the augmentation pipeline, e.g. 1.0 means the transform is always applied to all input images.</p> </div> <span> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab2.png?pub-status=live" class="aop-lazy-load-image" width="382" height="265" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab2.png" data-zoomable="false"></div> </span> </div> <p class="p"> </p><div class="table-wrap" data-magellan-destination="tbl3" id="tbl3"> <div class="caption"> <p class="p"><span class="label">Table 3.</span> List of hyperparameters used in SimCLR model training.</p> </div> <span> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab3.png?pub-status=live" class="aop-lazy-load-image" width="382" height="265" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab3.png" data-zoomable="false"></div> </span> </div> <p class="p"> Following Chen et al. (2020), all training runs began with a linear warm-up phase lasting 10 epochs, after which we switched to a cosine learning rate decay strategy. In total, we trained models for 500 epochs on the <span class="monospace">banner_smgps</span> and <span class="monospace">banner_emupilot</span> datasets. A smaller total number of epochs (100) was used when training over the larger <span class="monospace">hulk_smgps</span> and <span class="monospace">hulk_emupilot</span> datasets to reduce computational costs.</p> <p class="p"> Training runs were performed on three different computing server nodes, each equipped with a GPU device:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> Node A: 48 cores (Intel Xeon Gold 6248R CPU, 3.00 GHz), 512 GB RAM, NVIDIA Quadro RTX 6000 (24 GB)</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> Node B: 24 cores (Intel Xeon Silver 4410Y, 2.00 GHz), 256 GB RAM, NVIDIA A30 (24 GB)</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> Node C: 36 cores (Intel Xeon CPU E5-2697 v4, 2.30 GHz), 128 GB RAM, NVIDIA Tesla V100 (16 GB)</p> </li> </ul> <p class="p"> Typical training times over the <span class="monospace">hulk_smgps</span> dataset are of the order of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline73.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline73.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>6.7 hours/epoch on nodes A/B, and <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline74.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline74.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>12.5 hours/epoch on node C.</p> </div> <div class="sec" data-magellan-destination="s2-5" id="s2-5"> <h3 class="B"><span class="label">2.5</span> Evaluation of downstream tasks</h3> <p class="p"> In the following sections, the trained self-supervised models and corresponding data representation will be evaluated on radio source classification (<a class="xref sec" href="#s3">Section 3</a>) and detection (<a class="xref sec" href="#s4">Section 4</a>) tasks using supervised CNN classifiers trained on labelled datasets. Furthermore, in <a class="xref sec" href="#s5">Section 5</a> we will use the self-supervised features to classify radio images according to the morphology of hosted sources in a supervised way and according to their peculiarity degree in a completely unsupervised way. To estimate the performances achieved in these downstream tasks, we will consistently use these widely adopted metrics in multi-class problems:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">Recall</em> (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline75.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="13" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline75.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathcal{R}$ </span></span> </span> </span>): Fraction of sources (images) of a given class that were correctly classified by the model out of all sources (images) labelled in that class, computed as: </p><div data-mathjax-status="alt-graphic" class="disp-formula" data-magellan-destination="udisp1" id="udisp1"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU1.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="91" height="34" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU1.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> \begin{equation*}\mathcal{R}=\frac{TP}{TP + FN}\end{equation*} </span></span> </span> </div> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">Precision</em> (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline76.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline76.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathcal{P}$ </span></span> </span> </span>): Fraction of sources (images) correctly classified as belonging to a specific class, out of all sources (images) the model predicted to belong to that class, computed as:</p><div data-mathjax-status="alt-graphic" class="disp-formula" data-magellan-destination="udisp2" id="udisp2"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU2.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="87" height="34" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU2.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> \begin{equation*}\mathcal{P}=\frac{TP}{TP + FP}\end{equation*} </span></span> </span> </div> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">Contamination</em> (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline77.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline77.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\mathcal{C}$ </span></span> </span> </span>): Fraction of sources (images) of a given class incorrectly classified as belonging to a specific class, out of all sources (images) the model predicted to belong to that class, computed as: </p><div data-mathjax-status="alt-graphic" class="disp-formula" data-magellan-destination="udisp3" id="udisp3"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU3.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="142" height="33" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU3.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> \begin{equation*}\mathcal{C}= \frac{FP}{TP + FP}= 1 - \mathcal{P}\end{equation*} </span></span> </span> </div> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <em class="italic">F1-score</em>: the harmonic mean of precision and recall: </p><div data-mathjax-status="alt-graphic" class="disp-formula" data-magellan-destination="disp4" id="disp4"> <span class="disp-formula-label">(4)</span> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn4.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="145" height="34" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn4.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> \begin{equation}\text{F1-score}=2\times\frac{\mathcal{P}\times\mathcal{R}}{\mathcal{P}+\mathcal{R}}\end{equation} </span></span> </span> </div> </li> </ul> <p class="p"> where <em class="italic">TP</em>, <em class="italic">FN</em>, <em class="italic">FP</em> are the number of true positive, false negative and false positive instances, respectively.</p> </div> </div> <div class="sec other" data-magellan-destination="s3" id="s3"> <h2 class="A"><span class="label">3.</span> Task I: Classification of radio source morphology</h2> <p class="p"> In this section, we quantitatively evaluate the learned self-supervised representation on a source morphology classification problem.</p> <p class="p"> Morphological classification plays a pivotal role in radio astronomy, enabling scientists to gain insights into the underlying source nature from the observed shape and structures. The majority of existing works in the radio image domain are targeted for extragalactic science objectives, focusing on classification of radio galaxies (see for example Aniyan & Thorat <a class="xref bibr" href="#ref1"><span class="show-for-sr">Reference Aniyan and Thorat</span>2017</a>, Ma et al., <a class="xref bibr" href="#ref34"><span class="show-for-sr">Reference Ma</span>2019</a>, or Ndung’u et al., <a class="xref bibr" href="#ref39"><span class="show-for-sr">Reference Ndung’u</span>2023</a> for a recent review) in different morphological classes: <span class="monospace">compact</span>, <span class="monospace">FR-I</span>, <span class="monospace">FR-II</span>, <span class="monospace">bent-tailed</span> (including WAT<a class="xref fn" href="#fn5"><span class="show-for-sr">Footnote </span> <sup class="sup">e</sup> </a> and NAT<a class="xref fn" href="#fn6"><span class="show-for-sr">Footnote </span> <sup class="sup">f</sup> </a> population), <span class="monospace">irregular</span> (including, for example, X-shaped or ring-like radio galaxies).</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f3" id="f3"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig3.png?pub-status=live" class="aop-lazy-load-image" width="5187" height="3526" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig3.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 3.</span> Sample images from the RGZ dataset with representative sources of different morphological classes (reported below each frame). A zscale transform was applied to all images for visualization scopes.</p> </div></div></section> <p class="p"> Morphological classification is also an important post-detection stage to filter extracted sources by general morphology (e.g. compact vs extended sources) for specialized source property measurements or other advanced classification analysis. In this context, the adopted source labelling scheme is rather general-purpose and domain-agnostic, suited to be eventually refined afterwards. For example, typical used labels are <span class="monospace">POINT-LIKE</span>, <span class="monospace">RESOLVED</span>, <span class="monospace">COMPACT</span>, <span class="monospace">EXTENDED</span> or labels that contain information about the number of radio components present in the extracted source (as in Wu et al., <a class="xref bibr" href="#ref58"><span class="show-for-sr">Reference Wu</span>2019</a>).</p> <p class="p"> The analysis carried out in this section falls into the second use-case scenario. This choice is mostly driven by existing datasets. Available annotated datasets for radio galaxy classification (mostly based on VLA FIRST survey data) are, in fact, rather limited in size (e.g. typically <100-200 images per class, <2000 images overall) and would currently prevent us from obtaining a robust evaluation of our self-supervised models over multiple test set realizations. For example, the <em class="italic">Mirabest</em> dataset (Porter & Scaife <a class="xref bibr" href="#ref44"><span class="show-for-sr">Reference Porter and Scaife</span>2023</a>) contains 1256 source images of balanced FR-I/FR-II radio galaxy classes, out of which 833 images constitute the “Confident” sample, and the rest (423 images) the “Uncertain” sample. On this dataset, Slijepcevic et al. (<a class="xref bibr" href="#ref50"><span class="show-for-sr">Reference Slijepcevic</span>2024</a>) reported an improvement of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline78.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline78.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>3-4% in classification performance of a self-supervised pre-trained model with respect to a fully supervised model trained from scratch on the “Confident” sample (or on a portion of it). Classification metrics were, however, estimated on the “Uncertain” sample, and hence the observed enhancement is due to less than 20 sources. We, therefore, opted for this work to use a larger dataset (roughly by one order of magnitude) and perform a similar analysis once a larger dataset is assembled within the ASKAP EMU survey.</p> <div class="sec" data-magellan-destination="s3-1" id="s3-1"> <h3 class="B"><span class="label">3.1</span> Dataset</h3> <p class="p"> For this analysis, we considered data from the Radio Galaxy Zoo (RGZ) project<a class="xref fn" href="#fn7"><span class="show-for-sr">Footnote </span> <sup class="sup">g</sup> </a> (Banfield et al., <a class="xref bibr" href="#ref2"><span class="show-for-sr">Reference Banfield</span>2015</a>). This includes radio images of size 3’<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline79.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline79.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span> 3’ from the VLA Faint Images of the Radio Sky at Twenty cm (FIRST) survey (1.4 GHz, angular resolution <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline80.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline80.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>5<sup class="sup">′′</sup>) (Becker et al., <a class="xref bibr" href="#ref3"><span class="show-for-sr">Reference Becker</span>1995</a>). Radio sources found in these images were labelled into multiple morphological classes, on the basis of the observed number of components (C) and peaks (P) (see Wu et al. <a class="xref bibr" href="#ref58"><span class="show-for-sr">Reference Wu</span>2019</a> for more details on the classification schema). Angular size is also available for each source.</p> <p class="p"> In this analysis, we extracted 82 084 image cutouts around radio sources that have been classified in the RGZ Data Release 1 (DR1) with a consensus level <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline81.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="11" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline81.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\ge$ </span></span> </span> </span>0.6 in the following classes: 1C-1P (55.0%), 1C-2P (20.9%), 1C-3P (1.9%), 2C-2P (17.6%), 2C-3P (2.0%), 3C-3P (2.5%). We assumed a cutout size equal to 1.5 <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline82.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline82.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span> the source angular size, as listed in the RGZ catalogue. A representative image of each source morphological category is shown in <a class="xref fig" href="#f3">Figure 3</a>.</p> <p class="p"> As the full dataset is largely unbalanced towards sources of class morphology 1C-1P, we randomly created <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline83.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="26" height="12" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline83.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $N_{sets}$ </span></span> </span> </span> = 5 balanced training and test sets having 1000 and 600 images per class, respectively. Both training and test set images were pre-processed as described in <a class="xref sec" href="#s2-3">Section 2.3</a> for the SimCLR model training.</p> </div> <div class="sec" data-magellan-destination="s3-2" id="s3-2"> <h3 class="B"><span class="label">3.2</span> Evaluation of self-supervised representation</h3> <p class="p"> In <a class="xref fig" href="#f4">Figure 4</a> we present a two-dimensional projection, obtained with the <em class="italic">Uniform Manifold Approximation and Projection</em> (UMAP) (McInnes et al., <a class="xref bibr" href="#ref35">2018</a>) dimensionality reduction algorithm, of the representation vector (original size equal to 512) produced by the trained <span class="monospace">smart_hulk_smgps</span> model on the RGZ dataset. As can be observed, the self-supervised model effectively groups sources of different morphological class in distinct areas of the latent space. No isolated clusters are discernible in the projected two-dimensional UMAP feature space, as well as in a PCA scatter plot of top-2 features (not shown here). Nevertheless, these or similar diagnostic plots, can be useful for potentially identifying possible image mislabeling in the dataset, e.g. sources that fall within a region that is predominantly populated by other classes.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f4" id="f4"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig4.png?pub-status=live" class="aop-lazy-load-image" width="2081" height="1966" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig4.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 4.</span> 2D UMAP projection of the data representation vector (size = 512) produced by the trained <span class="monospace">smart_hulk_smgps</span> model on the RGZ dataset.</p> </div></div></section> <p class="p"> We carried out a classification analysis using a CNN classifier with a standard architecture: a <em class="italic">ResNet18</em> backbone model (as in the SimCLR model) followed by a classification head. The latter consists of a single layer followed by a softmax activation, representing the predicted probability distribution over the set of classes. To evaluate the quality of the self-supervised representation, we froze the backbone model, setting and fixing its weights to those obtained in the trained SimCLR models, and trained only the classification head on RGZ training datasets for a limited number of epochs (30). We considered only rotation and flipping transformations as augmentation steps during the training.</p> <p class="p"> In <a class="xref fig" href="#f5">Figure 5</a> we report the classification F1-scores obtained on the test set by different self-supervised pre-trained models: <span class="monospace">hulk_smgps</span> (red squares), <span class="monospace">banner_smgps</span> (blue inverted triangles), <span class="monospace">smart_hulk_smgps</span> (green triangles), <span class="monospace">hulk_emupilot</span> (orange diamonds), <span class="monospace">banner_emupilot</span> (cyan asterisks). The reported values and their errors are respectively the F1-score mean and mean error computed over the available test sets. These metrics were compared against those obtained with a baseline model pre-trained on the <span class="monospace">ImageNet-1k</span> dataset<a class="xref fn" href="#fn8"><span class="show-for-sr">Footnote </span> <sup class="sup">h</sup> </a> Deng et al., <a class="xref bibr" href="#ref11"><span class="show-for-sr">Reference Deng</span>2009</a>) (trained on non-radio data), shown with black dots in <a class="xref fig" href="#f5">Figure 5</a>. We found that self-supervised pre-trained models reach approximately 7–12% better overall scores with respect to the baseline, due to the higher quality features obtained on complex and extended sources, which are not as well represented in the <em class="italic">ImageNet</em> dataset. Another valuable indication is that the two-step pre-training approach done for the <span class="monospace">smart_hulk_smgps</span> model training provide better results compared to training over random or source-centred images alone. The improvement is, however, not very significant with respect to the <span class="monospace">hulk_smgps</span>, likely due to both the limited size of the <span class="monospace">banner_smgps</span> dataset and the absence of Galactic-like diffuse and extended sources in the RGZ dataset. By construction, we expect that the <span class="monospace">banner_smgps</span> model should be more specialized for this kind of source morphologies. This will be tested in a future analysis once we finalize a new test dataset with diffuse sources taken from ASKAP EMU observations.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f5" id="f5"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig5.png?pub-status=live" class="aop-lazy-load-image" width="2163" height="1865" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig5.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 5.</span> Classification F1-scores obtained for different classes and for all classes cumulatively over RGZ test sets with different pre-trained and frozen backbone models: <span class="monospace">hulk_smgps</span> (red squares), <span class="monospace">banner_smgps</span> (blue inverted triangles), <span class="monospace">smart_hulk_smgps</span> (green triangles), <span class="monospace">hulk_emupilot</span> (orange diamonds), <span class="monospace">banner_emupilot</span> (cyan asterisks), <span class="monospace">ImageNet</span> (black dots). The reported values and errors are the F1-score mean and mean error computed over five test sets.</p> </div></div></section> <p class="p"> In <a class="xref fig" href="#f6">Figure 6</a> we report the confusion matrix obtained over the RGZ test sample with a <span class="monospace">hulk_smgps</span> pre-trained and frozen backbone model. The obtained misclassification rates suggest that a considerable fraction (10% to 20%) of sources, particularly those with two or three components, may be hard to be correctly distinguished from other classes. After a visual inspection of the misclassified sources, we found that in some cases the misclassification is rather due to dataset mislabelling, e.g. the ground truth label present in the dataset is not correct and the model is indeed predicting the expected class. Some examples are reported in <a class="xref fig" href="#f13">Figure A.1</a>. Future analysis should therefore take into consideration a revision of the RGZ dataset annotation.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f6" id="f6"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig6.png?pub-status=live" class="aop-lazy-load-image" width="2427" height="1911" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig6.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 6.</span> Confusion matrix of the source morphology classifier (trained with <span class="monospace">smart_hulk_smgps</span> pre-trained and frozen backbone model) obtained over the RGZ test set.</p> </div></div></section> </div> <div class="sec" data-magellan-destination="s3-3" id="s3-3"> <h3 class="B"><span class="label">3.3</span> Model fine-tuning</h3> <p class="p"> We fine-tuned the source classifier by unfreezing backbone model layers (e.g. training them along with the classification head) and compared the accuracies reached by two models: one initialized with random weights (e.g. training from <em class="italic">scratch</em>), and the other with backbone model weights initialized to the <span class="monospace">smart_hulk_smgps</span> backbone model weights (best performing model found in <a class="xref sec" href="#s3-2">Section 3.2</a>). We compared the results of both models when trained on the full training sets and when trained on smaller training sets, obtained by gradually removing labelled data randomly from the original set. In all cases, models were trained for 150 epochs. The test sets were kept unchanged to compute the classification accuracies. This was done to study how the model performs in the recurring scenario in which the amount of labelled data is significantly limited. We reported the results in <a class="xref fig" href="#f7">Figure 7</a>. As can be seen, the fully supervised model (trained from scratch) becomes almost untrainable, providing poor classification metrics, in the small number of labels regime. This occurs for the RGZ dataset below a fraction of approximately 10% of the original training dataset, corresponding to about 600 images (e.g. <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline84.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline84.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>100 images per class). On the other hand, self-supervised pre-training enables to fine-tune the model even with few labels, achieving considerably better metrics (>20%). Above the 10% label fraction threshold, the fully supervised model achieved slightly better scores, highlighting that no significant performance benefits are obtained from the pre-training process, at least with the model and dataset sample sizes available for this work. This result is qualitatively on par with the results of the transfer learning analysis carried out by Chen et al. (2020) (Section B.8.2) on 12 natural image datasets (Food, CIFAR10, CIFAR100,) with <em class="italic">ResNet50</em> architectures of different widths (x1, x2, x4). The authors compared the fine-tuning classification accuracies reached by SimCLR against a supervised model baseline. With wider networks (<em class="italic">ResNet50</em> x4), the self-supervised model was found to outperform the supervised one in 7 datasets (Chen et al. 2020, Table 8). The opposite was however observed with the narrower <em class="italic">ResNet50</em>, where the supervised baseline best performed in 10 datasets (Chen et al. 2020, Table B5) out of 12. Our analysis, carried out with an even smaller network (<em class="italic">ResNet18</em>), may well fall into the latter case. In either cases, the observed accuracy differences are smaller than 1% for most datasets.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f7" id="f7"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig7.png?pub-status=live" class="aop-lazy-load-image" width="2156" height="2170" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig7.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 7.</span> Classification F1-scores obtained (for all classes cumulatively) over RGZ test sets as a function of the number of images <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline85.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="30" height="10" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline85.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $n_{train}$ </span></span> </span> </span> in the training set with two alternative models: one trained from scratch (open black dots), the other trained with backbone model weights initialized to <span class="monospace">smart_hulk_smgps</span> weights (filled black dots). The upper x-axis indicates the fraction of the full training set considered in each training run.</p> </div></div></section> </div> </div> <div class="sec other" data-magellan-destination="s4" id="s4"> <h2 class="A"><span class="label">4.</span> Task II: Radio source detection</h2> <p class="p"> In this section, we quantitatively evaluate the learned self-supervised representation on an instance segmentation problem, specifically the detection of radio sources with various morphologies.</p> <p class="p"> Algorithms used in traditional radio source finders are not well-suited for detecting extended radio sources with diffuse edges, and they are unable to detect extended sources that are composed of multiple disjoint regions. To address this limitation, new source finders (Wu et al., <a class="xref bibr" href="#ref58"><span class="show-for-sr">Reference Wu</span>2019</a>; Mostert et al., <a class="xref bibr" href="#ref38"><span class="show-for-sr">Reference Mostert</span>2022</a>; Zhang et al., <a class="xref bibr" href="#ref59"><span class="show-for-sr">Reference Zhang</span>2022</a>; Yu et al., <a class="xref bibr" href="#ref56"><span class="show-for-sr">Reference Yu</span>2022</a>; Riggi et al., <a class="xref bibr" href="#ref47"><span class="show-for-sr">Reference Riggi</span>2023</a>; Lao et al., <a class="xref bibr" href="#ref28"><span class="show-for-sr">Reference Lao</span>2023</a>; Gupta et al., <a class="xref bibr" href="#ref17"><span class="show-for-sr">Reference Gupta</span>2024</a>; Cornu et al., <a class="xref bibr" href="#ref10"><span class="show-for-sr">Reference Cornu</span>2024</a>) based on deep neural networks and object detection frameworks have been developed and trained on either simulated or real radio data. Core components of these models are deep CNN backbones and transformer architectures, both of which have millions of parameters that need to be optimized during training. Although these models offer a substantial advancement in extended radio galaxy detection, their performance is limited by the small size (few thousand images) and the imbalance of objects in the available radio training datasets. Additionally, there is a potential performance drop (up to 10% in Riggi et al., <a class="xref bibr" href="#ref47"><span class="show-for-sr">Reference Riggi</span>2023</a>) when transferring a trained model to data produced by a different survey or telescope, especially if the new data has a better angular resolution (Tang et al., <a class="xref bibr" href="#ref52"><span class="show-for-sr">Reference Tang</span>2019</a>). To improve the training stage, it is a common practice to use models pre-trained on much larger annotated samples of non-astronomical images, such as the <em class="italic">ImageNet-1k</em> (Deng et al., <a class="xref bibr" href="#ref11"><span class="show-for-sr">Reference Deng</span>2009</a>, <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline86.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline86.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>1.28 million images) or the <em class="italic">COCO</em> (Tsung-Yi et al. <a class="xref bibr" href="#ref53"><span class="show-for-sr">Reference Tsung-Yi</span>2014</a>, 328 000 images) datasets. In this scenario, it is worth exploring whether foundational models built with self-supervised methods on unlabelled radio data can offer performance benefits over non-radio foundational models, especially with small datasets.</p> <div class="sec" data-magellan-destination="s4-1" id="s4-1"> <h3 class="B"><span class="label">4.1</span> caesar-mrcnn source detector</h3> <p class="p"> For this analysis, we used the <em class="italic">caesar-mrcnn</em> source detector (Riggi et al., <a class="xref bibr" href="#ref47"><span class="show-for-sr">Reference Riggi</span>2023</a>), based on the Mask R-CNN object detection framework (He et al., <a class="xref bibr" href="#ref23"><span class="show-for-sr">Reference He</span>2017</a>), to extract source segmentation masks and predicted class labels from input radio images. With respect to our original work (Riggi et al., <a class="xref bibr" href="#ref47"><span class="show-for-sr">Reference Riggi</span>2023</a>), we have upgraded the software to TensorFlow 2.x, producing a new refactored version<a class="xref fn" href="#fn9"><span class="show-for-sr">Footnote </span> <sup class="sup">i</sup> </a> with an improved data pre-processing pipeline and support for additional backbone models.</p> <p class="p"> In this context, we would like to make a brief preamble and clarify the motivations that guided the development of the <em class="italic">caesar-mrcnn</em> source detector, as these were either misinterpreted or inaccurately presented in other works. Additionally, we aim to address certain conceptual aspects that we realize are often source of confusion within this field.</p> <p class="p"> It is essential to recognize that source detection (or extraction), classification and source characterization (or measurement) represent distinct conceptual stages. A source detector, to be defined as such, should focus solely on extracting source bounding boxes or, preferably, pixel masks, which are the inputs required for the source measurement or classification stages. The source measurement step, on the other hand, is responsible for estimating source properties such as position, flux density, and shape from the outputs of the source detection. Strictly speaking, this step is not required in a source detector, as assumed in Lao et al. (<a class="xref bibr" href="#ref28"><span class="show-for-sr">Reference Lao</span>2023</a>). From a methodological standpoint, it is advisable to avoid conflating these stages. This may allow addressing numerous use cases simultaneously, but it can also be counterproductive, leading, for example, to design compromises and overly complex models with multiple loss components to be balanced during training. The resulting models likely have a higher chance of underperforming on both tasks (detection or characterization) with respect to models that are designed and optimised for a specific task. For this reason, source characterization metrics should be independently evaluated and not mixed with the detection metrics, as required, for example, in the SKA Data Challenge 1 (Bonaldi et al., <a class="xref bibr" href="#ref5"><span class="show-for-sr">Reference Bonaldi</span>2021</a>) scoring function. When we designed the <em class="italic">caesar-mrcnn</em> source detector, we deliberately did not provide a source characterization stage. As we already implemented source measurement functions in the <em class="italic">caesar</em> source finder, we rather aim to interface both codes and, at best, add new developments for improvements in specific areas, such as low S/N source characterization and source deblending, as discussed in Boyce et al. (<a class="xref bibr" href="#ref8"><span class="show-for-sr">Reference Boyce</span>2023</a>).</p> <p class="p"> In recent ML-based source extractors, source classification was typically performed alongside the detection step, often to classify extracted sources into compact and extended classes of radio galaxies (FR-I, FR-II, etc.). We aimed for our source detector to be general-purpose, portable, and not tied to a specific radioastronomical domain. Therefore, in our view, the detection step should, at a minimum, classify between real and spurious sources, or, at most, between domain-agnostic morphological classes. More refined or domain-specific classification schemes can be more effectively applied afterwards in specialized classifiers working on source-centered images obtained from the detection step. These considerations were the rationale behind the general class labeling scheme adopted in <em class="italic">caesar-mrcnn</em> (briefly reported in the following Section).</p> </div> <div class="sec" data-magellan-destination="s4-2" id="s4-2"> <h3 class="B"><span class="label">4.2</span> Dataset</h3> <p class="p"> To train and test <em class="italic">caesar-mrcnn</em>, we considered the dataset described in Riggi et al., <a class="xref bibr" href="#ref47"><span class="show-for-sr">Reference Riggi</span>2023</a>), which contains 12 774 annotated radio images from different surveys, including VLA FIRST, ATCA Scorpio (Umana et al., <a class="xref bibr" href="#ref54"><span class="show-for-sr">Reference Umana</span>2015</a>), and ASKAP-EMU Scorpio (Umana et al., <a class="xref bibr" href="#ref55"><span class="show-for-sr">Reference Umana</span>2021</a>). The annotation data consist of pixel segmentation masks and classification labels for a total of 38 342 objects (both real and spurious sources) present in the dataset images. Five object classes were defined:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">SPURIOUS</span>: imaging artefacts around bright sources, having a ring-like or elongated compact morphology;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">COMPACT</span>: single-island isolated point- or slightly resolved compact radio sources with one or more blended components, each with morphology similar to the synthesized beam shape;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">EXTENDED</span>: radio sources with a single-island extended morphology, with one or more blended components, some morphologically different from the synthesized beam shape;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">EXTENDED-MULTISLAND</span>: radio sources with an extended morphology, consisting of more than one island, each eventually containing one or more blended components, having a point-like or an extended morphology;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">FLAGGED</span>: poorly-imaged single-island radio sources, highly contaminated by nearby imaging artefacts.</p> </li> </ul> <p class="p"> For more details on the dataset labelling schema and rationale, we refer the reader to the original work. We also define a generic class label <span class="monospace">SOURCE</span> for analysis purposes, including real and non-flagged sources, i.e. object instances of class <span class="monospace">COMPACT</span>, <span class="monospace">EXTENDED</span>, or <span class="monospace">EXTENDED-MULTISLAND</span>. Though it is planned, the dataset does not presently contain images and annotation data for Galactic diffuse objects. Indeed, none of existing ML-based finders have been trained to detect diffuse sources other than radio galaxy diffuse structures (e.g. lobe components). The latter are the only diffuse structures present in our dataset, but we never noted to obtain poor detection performances on them, as reported in Ndung’u et al. (<a class="xref bibr" href="#ref39"><span class="show-for-sr">Reference Ndung’u</span>2023</a>).</p> <p class="p"> In <a class="xref fig" href="#f8">Figure 8</a> we present sample images from the dataset, including representative sources for each class. Given that the current dataset is significantly skewed towards compact sources (comprising approximately 80% of the annotated objects), we created five re-balanced training samples, each containing 3245 images, with the following class distributions: <span class="monospace">SPURIOUS</span> (1464 objects, 14.4%), <span class="monospace">COMPACT</span> (5457 objects, 53.6%), <span class="monospace">EXTENDED</span> (2042 objects, 20.1%), <span class="monospace">EXTENDED-MULTISLAND</span> (1047, 10.3%), <span class="monospace">FLAGGED</span> (169 objects, 1.7%). The remaining data was reserved to create five test samples, each containing 5110 images, with the following class distributions: <span class="monospace">SPURIOUS</span> (1022 objects, 6.6%), <span class="monospace">COMPACT</span> (12.346 objects, 80.0%), <span class="monospace">EXTENDED</span> (1307 objects, 8.5%), <span class="monospace">EXTENDED-MULTISLAND</span> (636, 4.1%), <span class="monospace">FLAGGED</span> (122 objects, 0.8%).</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f8" id="f8"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig8.png?pub-status=live" class="aop-lazy-load-image" width="5186" height="1392" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig8.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 8.</span> Sample images (taken from Riggi <a class="xref bibr" href="#ref47"><span class="show-for-sr">Reference Riggi</span>2023</a>) from the dataset used for <em class="italic">caesar-mrcnn</em> training/testing, including objects of different classes: a <span class="monospace">FLAGGED</span> object (<a class="xref fig" href="#f8">Figure 8</a>(a), in gray), <span class="monospace">COMPACT</span> objects (in blue), a <span class="monospace">MULTI-ISLAND</span> object (<a class="xref fig" href="#f8">Figure 8</a>(b), in orange), <span class="monospace">EXTENDED</span> objects (<a class="xref fig" href="#f8">Figure 8</a>(c), in yellow), <span class="monospace">SPURIOUS</span> objects (<a class="xref fig" href="#f8">Figure 8</a>(d), in red).</p> </div></div></section> </div> <div class="sec" data-magellan-destination="s4-3" id="s4-3"> <h3 class="B"><span class="label">4.3</span> Evaluation of self-supervised representation</h3> <p class="p"> To assess the effectiveness of the self-supervised representation, we followed the procedure outlined in <a class="xref sec" href="#s3-2">Section 3.2</a>. We froze the Mask R-CNN <em class="italic">ResNet18</em> backbone model, setting and keeping its weights fixed to those obtained in the trained SimCLR models, and trained the remaining components (region proposal network, classification and bounding box regression head, mask prediction head) on multiple training datasets for a set number of epochs (250). The parameters of Mask R-CNN were configured to match the values optimized in our previous work (refer to Riggi <a class="xref bibr" href="#ref47"><span class="show-for-sr">Reference Riggi</span>2023</a>, Table A1). We applied the same pre-processing transformations used for training the self-supervised models (as detailed in <a class="xref sec" href="#s2-3">Section 2.3</a>). During training, we applied three distinct image augmentations: rotation, horizontal/vertical flipping, and zscale transformation with random contrast in the range of 0.25 to 0.4.</p> <p class="p"> The performance of source detection was evaluated on the test sets using the metrics<a class="xref fn" href="#fn10"><span class="show-for-sr">Footnote </span> <sup class="sup">j</sup> </a> defined in <a class="xref sec" href="#s2-5">Section 2.5</a> and the following detection/classification criteria:</p><ol class="list number nomark"> <li class="list-item"> <p class="p"><span class="label">1.</span> Object detection score threshold equal to 0.5;</p> </li> <li class="list-item"> <p class="p"><span class="label">2.</span> Intersection-over-Union (IoU) match threshold between detected and ground truth object masks equal to 0.6;</p> </li> <li class="list-item"> <p class="p"><span class="label">3.</span> Object classified in the <span class="monospace">SOURCE</span> class group.</p> </li> </ol> <p class="p"> </p><section><div class="fig" data-magellan-destination="f9" id="f9"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig9.png?pub-status=live" class="aop-lazy-load-image" width="2214" height="2068" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig9.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 9.</span> Mask R-CNN object detection F1-score metric obtained for different object classes over multiple test sets with different pre-trained and frozen backbone models: <span class="monospace">hulk_smgps</span> (red squares), <span class="monospace">banner_smgps</span> (blue iverted triangles), <span class="monospace">smart_hulk_smgps</span> (green triangles), <span class="monospace">hulk_emupilot</span> (orange diamonds), <span class="monospace">banner_emupilot</span> (cyan asterisks), <span class="monospace">ImageNet</span> (black dots). The reported values and errors are the means and mean errors computed over 5 test sets.</p> </div></div></section> <p class="p"> The above metrics were computed for each class label and reported in <a class="xref fig" href="#f9">Figure 9</a> for different models trained with frozen self-supervised backbone model weights: <span class="monospace">hulk_smgps</span> (red squares), <span class="monospace">banner_smgps</span> (blue triangles), <span class="monospace">smart_hulk_smgps</span> (green triangles), <span class="monospace">hulk_emupilot</span> (orange diamonds). Metrics obtained with frozen <em class="italic">ImageNet</em> weights are shown with black dots. The performance boost obtained with self-supervised models is significant, around 15%-20% for most classes, and even larger for multi-island sources and imaging artefacts. This is somehow expected, given that these structures are not present in the <em class="italic">ImageNet</em> dataset. Overall, for the source class group we are interested in, we did not notice significant differences among trained self-supervised models, after taking into account the run-to-run statistical uncertainties on the obtained metrics. We will therefore consider a representative model (<span class="monospace">hulk_smgps</span>) in the following fine-tuning analysis.</p> </div> <div class="sec" data-magellan-destination="s4-4" id="s4-4"> <h3 class="B"><span class="label">4.4</span> Model fine-tuning</h3> <p class="p"> We fine-tuned the Mask R-CNN model using random initialization weights (training from <em class="italic">scratch</em>) and weights initialized to <span class="monospace">hulk_smgps</span> self-supervised model. We computed the object detection metrics over the source class group as a function of the training sample size, following the same approach discussed in <a class="xref sec" href="#s3-3">Section 3.3</a>. Results are reported in <a class="xref fig" href="#f10">Figure 10</a>. Black filled dots are the F1-scores obtained with the pre-trained <span class="monospace">hulk_smgps</span> model, while open black dots are those found when training from scratch. In this case, we did not observe a significant benefit from using self-supervised pre-training compared to the source classification task studied in <a class="xref sec" href="#s3">Section 3</a>. The improvement in performance in the low label regime (<10% of the original training sample size) is, in fact, of the order of a few percent. This behaviour highlights that other Mask R-CNN components likely play a major role in the overall model detection performance with respect to the backbone model.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f10" id="f10"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig10.png?pub-status=live" class="aop-lazy-load-image" width="2156" height="2170" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig10.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 10.</span> Mask R-CNN object detection F1-score metric obtained over the <span class="monospace">SOURCE</span> class over multiple test sets as a function of the number of images <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline87.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="30" height="10" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline87.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $n_{train}$ </span></span> </span> </span> in the training set with two alternative models: one trained from scratch (open markers), the other trained with backbone model weights initialized to <span class="monospace">hulk_smgps</span> weights (filled markers). The upper x-axis indicates the fraction of the full training set considered in each training run.</p> </div></div></section> </div> </div> <div class="sec other" data-magellan-destination="s5" id="s5"> <h2 class="A"><span class="label">5.</span> Task III: Search for peculiar objects</h2> <p class="p"> In this section, we quantitatively evaluated the learned self-supervised representations in an anomaly detection problem, i.e. employing them for an unsupervised search of radio objects with peculiar morphologies.</p> <p class="p"> Next-generation radio surveys carried out with SKA precursor telescopes are already generating a huge amount of data. Serendipitous discoveries were already reported and obtained by visual inspection of the observed maps. For instance, Norris et al. (<a class="xref bibr" href="#ref42"><span class="show-for-sr">Reference Norris</span>2021</a>b) and Koribalski et al. (<a class="xref bibr" href="#ref26"><span class="show-for-sr">Reference Koribalski</span>2021</a>) discovered a class of diffuse objects with a roundish shape, dubbed <em class="italic">Odd Radio Circles</em> (ORCs), in the ASKAP EMU pilot survey, that did not correspond to any types of object or artifacts known to have similar morphological features. As it is extremely likely that new discoveries are still waiting to be found in such data deluge, astronomers have started to explore ML-based methods to automatically search for objects with peculiar morphologies. In this process, various methods were proposed, allowing to rediscover previously identified anomalies (including the first detected ORCs) and identify completely new objects (Gupta et al., <a class="xref bibr" href="#ref19"><span class="show-for-sr">Reference Gupta</span>2022</a>; Lochner et al., <a class="xref bibr" href="#ref30"><span class="show-for-sr">Reference Lochner</span>2023</a>).</p> <p class="p"> In this context, two major methodologies were used. Gupta et al. (<a class="xref bibr" href="#ref19"><span class="show-for-sr">Reference Gupta</span>2022</a>) and Mostert et al. (<a class="xref bibr" href="#ref37"><span class="show-for-sr">Reference Mostert</span>2021</a>) employed rotation and flipping invariant self-organizing maps (SOMs) to search for anomalies in the ASKAP EMU pilot and LOFAR LoTSS survey data, respectively. Both analysis used images of fixed size (approximately 1’ to 5’, <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline88.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline88.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>150 pixels per size), centered around previously catalogued radio sources. The Euclidean distance from each “representative” image in the SOM lattice was used as an “anomaly proxy”, e.g. anomalous images have larger Euclidean distances from their closest SOM template image.</p> <p class="p"> Segal et al. (<a class="xref bibr" href="#ref48"><span class="show-for-sr">Reference Segal</span>2023</a>) used a coarse-grained complexity metric as an “anomaly” proxy to detect peculiar objects in the ASKAP EMU pilot survey. Their method is based on the idea that image frames containing complex and anomalous objects have a higher Kolmogorov complexity compared to ordinary frames. In contrast to the previously mentioned methods, Segal et al. (<a class="xref bibr" href="#ref48"><span class="show-for-sr">Reference Segal</span>2023</a>) conducted a blind search by sliding fixed image frames of size 256<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline89.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline89.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span>256 pixels (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline90.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline90.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>12 arcmin) through the entire map, rather than focusing on frames centered around known source positions. An approximated complexity estimation for each frame was then computed from the compression file size (using the gzip algorithm) of smoothed and resized frames. This allowed the authors to obtain a catalogue of peculiar sources at different reliability levels, corresponding to different complexity threshold choices. The complexity metric is conceptually simple and fast to compute, which is undoubtedly a positive aspect of this method. However, as noted by Mostert et al. (<a class="xref bibr" href="#ref37"><span class="show-for-sr">Reference Mostert</span>2021</a>), the complexity metric may not fully capture the morphological features of the sources present in the images.</p> <p class="p"> A potential limitation of “source-centric” approaches could be their reliance on catalogues created with traditional source finding algorithms, which are known to have a higher likelihood of missing diffuse sources (a primary target in anomaly searches). Nevertheless, existing studies successfully manage to identify new anomalous sources in their datasets. Mostert et al. (<a class="xref bibr" href="#ref37"><span class="show-for-sr">Reference Mostert</span>2021</a>) also noted that their method is not fully sensitive to detect anomalies at angular scales much smaller than the chosen image size (100 arcsec in their work). The choice of the frame size is an aspect that certainly affects “blind” anomaly searches as well.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f11" id="f11"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig11.png?pub-status=live" class="aop-lazy-load-image" width="5188" height="3577" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig11.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 11.</span> Sample images from the <span class="monospace">hulk_emupilot</span> dataset, labelled as <span class="monospace">PECULIAR</span> and <span class="monospace">COMPACT</span>. The other assigned labels are reported below each frame. A zscale transform was applied to all images for visualization scopes.</p> </div></div></section> <p class="p"> In this work, we aim to carry out a blind anomaly search study using a different method, which relies on image features extracted by trained self-supervised models. Details on the dataset used and the methodology are provided in the following paragraphs.</p> <div class="sec" data-magellan-destination="s5-1" id="s5-1"> <h3 class="B"><span class="label">5.1</span> Dataset</h3> <p class="p"> For this analysis, we considered the <span class="monospace">hulk_emupilot</span> dataset (55,774 images) described in <a class="xref sec" href="#s2-2">Section 2.2</a>. We annotated through visual inspection approximately 10% of the data (5800 images) using the following set of labels:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">BACKGROUND</span>: If the image is purely background noise, e.g. no sources are visible. Typically, this label is set for frames located at the map borders;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">COMPACT</span>: if point sources or compact sources comparable with the synthesized beam size (say <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline91.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline91.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $ \lt $ </span></span> </span> </span>10 times the beam) are present. Double or triple sources with point-like components also fall into this category;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">EXTENDED</span>: if any extended source is visible, e.g. a compact source with extension <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline92.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline92.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $ \gt $ </span></span> </span> </span>10 <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline93.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="9" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline93.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\times$ </span></span> </span> </span> beam;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">RADIO-GALAXY</span>: if any extended source is visible with a single- or multi-island morphology, suggesting that of a radio galaxy (e.g. core + lobes);</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">DIFFUSE</span>: if any diffuse source is visible, typically having small-scale (e.g. <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline94.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline94.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $ \lt $ </span></span> </span> </span>few arcmin) and roundish morphology;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">DIFFUSE-LARGE</span>: if any large-scale (e.g. covering half of the image) diffuse object with irregular shape is visible;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">FILAMENT</span>: if any extended filamentary structures is visible;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">ARTEFACT</span>: if any ring-shaped or ray-like artefact is visible, e.g. typically around bright resolved sources;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">PECULIAR</span>: if any object is found with peculiar/anomalous morphology;</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">MOSAICKING</span>: if any residual pattern of the mosaicking process used to produce the image is present.</p> </li> </ul> <p class="p"> More than one label can be assigned to each image, depending on the object/features the user recognize in the image.</p> <p class="p"> A total of 428 peculiar frames were selected through visual inspection starting from a list of 1198 peculiar frames identified in Segal et al. (<a class="xref bibr" href="#ref48"><span class="show-for-sr">Reference Segal</span>2023</a>) with a complexity metric analysis and from a catalogue of 361 peculiar sources reported in Gupta et al. (<a class="xref bibr" href="#ref17"><span class="show-for-sr">Reference Gupta</span>2024</a>). In <a class="xref fig" href="#f11">Figure 11</a> we show examples of peculiar images from the dataset with their annotation labels.</p> <p class="p"> </p><section><div class="fig" data-magellan-destination="f12" id="f12"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig12.png?pub-status=live" class="aop-lazy-load-image" width="4667" height="1969" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig12.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure 12.</span> Left: Anomaly score of frames contained in the <span class="monospace">hulk_emupilot</span> dataset, shown as black solid histogram, found with the <em class="italic">Isolation Forest</em> algorithm over top-10 feature data. Unclassified frames are shown with a dashed line. Red filled histogram are the scores of peculiar frames. Ordinary frames (e.g. hosting only compact or artefacts) are shown in blue, pure compact frames in light blue, while frames not tagged as peculiar that host complex sources or structures (<span class="monospace">EXTENDED</span>, <span class="monospace">DIFFUSE</span>, <span class="monospace">DIFFUSE-LARGE</span>, <span class="monospace">RADIO-GALAXY</span>) are shown in green. Right: Anomaly detection metrics (recall, precision, contamination) as a function of the applied anomaly score threshold. Red solid and dashed lines indicate the recall and precision achieved on peculiar frame detection. Purple dotted line is the precision obtained over both peculiar and complex frames. The other solid coloured lines indicate the fraction of unclassified (black line), complex (green line) and ordinary frames contaminating the selected anomaly sample.</p> </div></div></section> </div> <div class="sec" data-magellan-destination="s5-2" id="s5-2"> <h3 class="B"><span class="label">5.2</span> Anomaly analysis</h3> <p class="p"> The data representation variables are each sensitive to different features of the images, including details (e.g. the presence of image borders or artifacts, background noise or mosaicking patterns, compact source density, etc) that are not relevant for the anomaly search task. We tried to limit the dependency on background features with the <em class="italic">RandomThresholding</em> augmentation, but the model was not fully made invariant with respect to the other aspects. For this reason, we carried out a feature selection analysis, aiming to explore and select features that are mostly correlated with the presence of objects with diffuse or extended morphology. We divided the labelled set of images into two groups: “interesting” frames include images labelled as {<span class="monospace">EXTENDED</span>,<span class="monospace">DIFFUSE</span>,<span class="monospace">DIFFUSE-LARGE</span>}, while “ordinary” frames include the rest of labelled images, mostly hosting only compact sources or artifacts around them. We then trained a LightGBM<a class="xref fn" href="#fn11"><span class="show-for-sr">Footnote </span> <sup class="sup">k</sup> </a> (Ke et al., <a class="xref bibr" href="#ref25"><span class="show-for-sr">Reference Ke</span>2017</a>) classifier to classify the two groups with all representation features (512) as inputs. A subset of available data was reserved as a cross-validation set for model training early stop. Using shallow decision trees (<span class="monospace">max_depth</span>=2) and default LightGBM parameters (<span class="monospace">num_leaves</span>=32, <span class="monospace">min_data_in_leaf</span>=20), we obtained a classification F1-score of 75.3%. In <a class="xref fig" href="#f14">Figure A.2</a> we report a plot showing the feature importance returned by the LightGBM trained model. As one can see, a small set of features are identified as the most powerful for selecting interesting frames. We therefore carried out the following data exploration and unsupervised analysis, restricting the parameter set to the top-15 ranked variables in importance.</p> <p class="p"> In <a class="xref fig" href="#f3">Figure 3</a>(a) we report a two-dimensional projection of the top-15 variables produced with the UMAP algorithm as a function of the image noise rms level in logarithmic scale (coloured z-axis). As can be seen, the obtained representation shows a residual dependency on physical image parameters, such as the noise rms, that cannot be fully removed by the augmentation scheme currently adopted. In the other panels of <a class="xref fig" href="#f14">Figure A.3</a> we report the same projection for unlabelled (gray markers) and labelled data, shown with coloured markers. Interestingly, frames that were labelled as peculiar or complex (e.g. containing extended/diffuse objects or artifacts) tend to cluster in specific areas of the projected feature space, also related with higher noise areas, while ordinary frames are uniformly spread in the feature space. Other higher noise areas present in <a class="xref fig" href="#f3">Figure 3</a>(a) seem related to frames that are closer to the mosaic edges or having artifacts (see <a class="xref fig" href="#f3">Figure 3</a>(b)).</p> <p class="p"> We searched for peculiar frames using the <em class="italic">Isolation Forest</em> (IF) (Liu et al., <a class="xref bibr" href="#ref31"><span class="show-for-sr">Reference Liu</span>2008</a>) outlier detection algorithm<a class="xref fn" href="#fn12"><span class="show-for-sr">Footnote </span> <sup class="sup">l</sup> </a>. We tuned these IF hyperparameters using the annotated dataset:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">contamination</span>: The proportion of outliers in the data set. We scanned these values: ‘auto’, 0.001, 0.01, 0.1.</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> <span class="monospace">max_samples</span>: The number of samples to draw from the training data to train each base estimator. We scanned these values: ‘auto’, 0.001, 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0.</p> </li> </ul> <p class="p"> Scans were repeated for different choices of importance ranked feature sets: <span class="monospace">top2</span>, <span class="monospace">top5</span>, <span class="monospace">top10</span>, and <span class="monospace">top15</span>. A number of 200 base estimators were used in the tree ensemble. Other IF parameters were set to defaults. Best classification results were obtained with a smaller fraction of samples (<span class="monospace">max_samples</span>=0.02) and <span class="monospace">contamination</span>=0.001.</p> <p class="p"> We then ran the IF algorithm in an unsupervised way with tuned parameters and obtained an anomaly score for each dataset frame. The anomaly score ranges from 0 to 1, with most anomalous data expected to have values close to 1. In <a class="xref fig" href="#f12">Figure 12</a> (left panel) we report the distribution of IF anomaly scores of all frames contained in the <span class="monospace">hulk_emupilot</span> dataset, shown as a black solid histogram, found over top-10 feature data. Unclassified frames are shown with a dashed line. The red filled histogram indicates the labelled peculiar frames. Ordinary frames (e.g. hosting only compact or artifacts) are shown in blue, pure compact frames in light blue, while complex frames (e.g. hosting extended or diffuse structures, not labelled as peculiar) are shown in green.</p> <p class="p"> Following <a class="xref sec" href="#s2-5">Section 2.5</a>, we computed the anomaly detection metrics (peculiar frame recall and precision, non-peculiar frame contamination) as a function of the applied anomaly score threshold. Peculiar frame recall and precision are reported in <a class="xref fig" href="#f12">Figure 12</a> (right panel) as a function of the applied anomaly score threshold for top-10 feature data, respectively shown with solid and dashed red lines. We also computed the precision in classifying detected frames as either peculiar or complex, shown with a dotted purple line. The other solid coloured lines indicate the fraction of unclassified (black line), complex (green line) and ordinary frames contaminating the selected anomaly sample. In <a class="xref table" href="#tbl4">Table 4</a> we summarized the metrics obtained for different feature sets for the anomaly score threshold that provides the best peculiar recall/precision compromise (e.g. the score at which recall and precision curves cross in <a class="xref fig" href="#f11">Figure 12</a>(b)). Best detection performances (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline95.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline95.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>60%) are obtained with the top-5 features, but the top-10 feature set currently provides the smallest contamination fraction of ordinary frames (<span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline96.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="10" height="8" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline96.png" data-zoomable="false"> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $ \lt $ </span></span> </span> </span>3%). When considering both peculiar and complex frames, the precision increases to 97%.</p> <p class="p"> </p><div class="table-wrap" data-magellan-destination="tbl4" id="tbl4"> <div class="caption"> <p class="p"><span class="label">Table 4.</span> Peculiar frame detection metrics obtained with the <em class="italic">Isolation Forest</em> algorithm over selected feature sets (column (1)) when using an anomaly score threshold (reported in column (2)) that provides the best compromise in terms of peculiar frame recall and precision, respectively shown in columns (3) and (4). The precision relative to joint peculiar and complex frames is shown in column (5). The fractions of complex and ordinary frames contaminating the predicted anomalous sample are shown in columns (6) and (7).</p> </div> <span> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab4.png?pub-status=live" class="aop-lazy-load-image" width="382" height="133" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab4.png" data-zoomable="false"></div> </span> </div> </div> <div class="sec" data-magellan-destination="s5-3" id="s5-3"> <h3 class="B"><span class="label">5.3</span> Astronomer-in-the-loop</h3> <p class="p"> It is worth to note that the source peculiarity concept is rather subjective and may depend on the scientific domain of interest. For instance, a fraction of complex frames may well be considered as truly peculiar in specific analysis, and, on the other hand, missed peculiar frames may be considered not as relevant in other contexts. For this reason, an additional “human-in-the-loop” processing stage has to be applied to our list of candidate anomalies to create a refined sample that better fits scientific needs.</p> <p class="p"> For the sake of demonstration, we integrated our dataset in the <span class="monospace">astronomaly</span> package<a class="xref fn" href="#fn13"><span class="show-for-sr">Footnote </span> <sup class="sup">m</sup> </a> (Lochner & Bassett, <a class="xref bibr" href="#ref29"><span class="show-for-sr">Reference Lochner and Bassett</span>2021</a>). This allowed us to run an active learning process from a web interface in which users can personalize and sort the list of anomalous frames on the basis of the computed score and also their expressed preferences, such as how peculiar a frame is judged on a scale of 1 to 5. A screenshot of the <span class="monospace">astronomaly</span> UI for our dataset is shown in <a class="xref fig" href="#f16">Figure A.4</a>.</p> <p class="p"> We plan to integrate in the future the full pipeline (feature extraction, anomaly detection, active learning loop) as a supported application within the <em class="italic">caesar-rest</em> service<a class="xref fn" href="#fn14"><span class="show-for-sr">Footnote </span> <sup class="sup">n</sup> </a> (Riggi <a class="xref bibr" href="#ref46"><span class="show-for-sr">Reference Riggi</span>2021</a>), and extend the web UI with missing functionalities (e.g. image filtering/exporting, model importing, configuration options, etc). In this study, we limited ourselves to primarily quantify the ordinary frame rejection power that can be currently achieved with self-supervised features, as this will largely impact the time needed to visually inspect the anomaly candidates in human-in-the-loop approaches to form the final anomaly sample.</p> </div> </div> <div class="sec other" data-magellan-destination="s6" id="s6"> <h2 class="A"><span class="label">6.</span> Summary</h2> <p class="p"> In this study, we investigated the potential of self-supervised learning for analysing radio continuum image data produced by SKA precursors. Specifically, we have used the SimCLR contrastive learning framework to train deep network models on large sets of unlabelled images extracted from the ASKAP EMU pilot and SARAO MeerKAT GPS surveys, either randomly selected or centred around catalogued extended source positions. The trained encoder network, based on the <em class="italic">ResNet18</em> architecture, was used as a feature extractor and fine-tuned for three distinct downstream tasks (source detection, morphology classification, and anomaly detection) over test datasets comprising thousands of annotated images from other radio surveys (VLA FIRST, ASKAP Early Science, ATCA Scorpio surveys). Notably, some of these test datasets were purposefully created for this work.</p> <p class="p"> All trained models, including both the source code and network weights, have been publicly released. These represent a first outcome of this work, as they can be viewed as prototypal radio foundational models, available to be used in future applications for multiple scopes:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> to extract feature parameters from new radio survey images and perform data inspection, unsupervised classification or outlier detection analysis (as demonstrated in <a class="xref sec" href="#s5">Section 5</a>);</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> to serve as pre-trained backbone components of more complex models designed for source classification, detection or other tasks (e.g. source property characterization), eventually refined over new labelled datasets (as demonstrated in <a class="xref sec" href="#s3">Sections 3</a> and <a class="xref sec" href="#s4">4</a>).</p> </li> </ul> <p class="p"> The analyses we performed in this work attempted to address various open questions in this field, paving the way for future analyses:</p><ul class="list nomark"> <li class="list-item"> <p class="p"><span class="label">•</span> Do we observe any advantages stemming from self-supervised models trained on easily constructed “random” survey datasets compared to costly-to-compile “source-centric” datasets?</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> How does self-supervised learning on radio data compare in performance to models pre-trained on extensive non-radio datasets, such as <em class="italic">ImageNet</em>?</p> </li> <li class="list-item"> <p class="p"><span class="label">•</span> Is it feasible to enhance existing radio source detectors utilizing deep networks through radio self-supervised pre-training?</p> </li> </ul> <p class="p"> We found that using uncurated large collections of unlabelled radio images randomly extracted from SKA precursor surveys resulted in significantly improved performances (approximately 5%) in both radio source detection and classification tasks, compared to curated (albeit smaller) image samples extracted around extended source catalogues. This indication, primarily attributed to the augmented number of accessible images achievable with uncurated collections, is highly encouraging, as it suggests that certain aspects of source analysis can be enhanced even without investing numerous work months in catalogue production.</p> <p class="p"> The advantages gained from self-supervised pre-training on radio data, compared to non-radio data, are notably significant (exceeding 10%) in both source classification and detection tasks. However, when contrasting our findings with fully supervised models trained from scratch, we observed that these benefits are only relevant with small labelled datasets (on the order of a few hundred images). This is certainly a positive aspect, considering that many available annotated datasets (such as <em class="italic">MiraBest</em> or similar radio galaxy classification datasets) typically fall within this size range. Nevertheless, in order to observe a substantial impact on larger datasets, it becomes imperative to improve both the self-supervised pre-training dataset and the model itself.</p> <p class="p"> We have identified some areas of developments to be made in the near future to improve source analysis performance, and overcome the limitations encountered in this study. Firstly, we plan to increase the size of our pre-training <span class="monospace">hulk</span> datasets, by leveraging the massive amount of unlabelled image data being delivered by large area surveys, such as ASKAP EMU, the Very Large Array Sky Survey (VLASS) (Lacy et al., <a class="xref bibr" href="#ref27"><span class="show-for-sr">Reference Lacy</span>2020</a>), or the LOFAR Two-metre Sky Survey (LoTSS) (Shimwell et al. <a class="xref bibr" href="#ref51"><span class="show-for-sr">Reference Shimwell</span>2017</a>) surveys. In this context, to reduce the computational load during training, it is crucial to explore effective and automated strategies for constructing semi-curated large-scale pre-training datasets, potentially comprising millions of images. This step may require the development of specialized algorithms to filter or weight image frames included in the pre-training dataset, aiming to maximize the balance between ordinary and complex objects “seen” by the model.</p> <p class="p"> Additionally, we have already started to train larger architectures and recent state-of-the-art self-supervised frameworks, particularly those based on Vision Transformers (ViTs), over the same datasets produced for this study. Results will be compared against the SimCLR baseline and presented in a forthcoming paper.</p> </div> </div> <div class="back"> <div class="ack"> <h2 class="A"> Acknowledgement</h2> <p class="p"> This scientific work uses data obtained from Inyarrimanha Ilgari Bundara/the Murchison Radio-astronomy Observatory. We acknowledge the Wajarri Yamaji People as the Traditional Owners and native title holders of the Observatory site. CSIRO’s ASKAP radio telescope is part of the Australia Telescope National Facility (<a class="uri" href="https://ror.org/05qajvd42">https://ror.org/05qajvd42</a>). Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing Research Centre. Establishment of ASKAP, Inyarrimanha Ilgari Bundara, the CSIRO Murchison Radio-astronomy Observatory and the Pawsey Supercomputing Research Centre are initiatives of the Australian Government, with support from the Government of Western Australia and the Science and Industry Endowment Fund.</p> <p class="p"> This work made use of PLEIADI, a computing infrastructure installed and managed by INAF.</p> </div> <div class="sec other" data-magellan-destination="s50" id="s50"> <h2 class="A"> Funding statement</h2> <p class="p"> This work received funding from the INAF CIRASA and SCIARADA projects.</p> </div> <div class="sec coi-statement" data-magellan-destination="s51" id="s51"> <h2 class="A"> Competing interests</h2> <p class="p"> None.</p> </div> <div class="sec data-availability" data-magellan-destination="s52" id="s52"> <h2 class="A"> Data availability statement</h2> <p class="p"> The software code used in this work is publicly available under the GNU General Public License v3.0<a class="xref fn" href="#fn15"><span class="show-for-sr">Footnote </span> <sup class="sup">o</sup> </a> on the GitHub repository <a class="uri" href="https://github.com/SKA-INAF/sclassifier/">https://github.com/SKA-INAF/sclassifier/</a>. The trained model weights have been made available on Zenodo repository at <a class="uri" href="https://doi.org/10.5281/zenodo.12636593">https://doi.org/10.5281/zenodo.12636593</a>.</p> </div> <div class="app-group" data-magellan-destination="appg1" id="appg1"> <h2 class="A">Appendix</h2> <div class="app" data-magellan-destination="app1" id="app1"> <h3 class="B"><span class="label">A.</span> Supplementary plots</h3> <p class="p"> </p><section><div class="fig" data-magellan-destination="f13" id="f13"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig13.png?pub-status=live" class="aop-lazy-load-image" width="5189" height="3508" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig13.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure A.1.</span> Examples of sources from the RGZ test dataset that were misclassified by the trained source classifier (<span class="monospace">hulk_smgps</span> pre-trained and frozen backbone model) due to an incorrect true class label provided in the dataset (mislabelling). The true and predicted class labels are reported below each frame. In many cases, the model indeed correctly predicted the expected true classification (denoted as “true corr.” below each frame).</p> </div></div></section> <p class="p"> </p><section><div class="fig" data-magellan-destination="f14" id="f14"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig14.png?pub-status=live" class="aop-lazy-load-image" width="2427" height="1598" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig14.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure A.2.</span> Feature importance obtained with a LightGBM classifier trained on <span class="monospace">hulk_emupilot</span> data representation, for the classification of interesting against ordinary images.</p> </div></div></section> <p class="p"> </p><section><div class="fig" data-magellan-destination="f15" id="f15"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig15.png?pub-status=live" class="aop-lazy-load-image" width="4375" height="4175" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig15.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure A.3.</span> Figure 14: 2D UMAP projection of the top-15 selected features from the data representation vector produced by the trained SimCLR model on the <span class="monospace">hulk_emupilot</span> dataset as a function of the image noise RMS level in logarithmic scale (z-scale axis). Red markers correspond to image with higher RMS levels, while blue markers to low noise RMS levels. Left: 2D UMAP projection of the top-15 selected features for unclassified frames (gray markers) and labelled frames (coloured markers, as reported in the plot legends). See text for details on label schema.</p> </div></div></section> <p class="p"> </p><section><div class="fig" data-magellan-destination="f16" id="f16"> <div class="figure-thumb"><img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig16.png?pub-status=live" class="aop-lazy-load-image" width="5187" height="2991" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig16.png" data-zoomable="true"></div> <div class="caption"><p class="p"> </p><p class="p"><span class="label">Figure A.4.</span> Screenshot of <span class="monospace">astronomaly</span> web UI with list of anomalous frames selected from the <span class="monospace">hulk_emupilot</span> dataset.</p> </div></div></section> </div> </div> </div> </div></div> <hr aria-hidden="true" class="list-divider separator default" data-v-7036083a> <div id="footnotes-list" class="circle-list"><h2>Footnotes</h2> <div data-type="fulltextNote" id="fn1" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup"> <sup class="sup">a</sup> </sup> </span> <a class="uri" href="https://www.zooniverse.org/projects/chrismrp/radio-galaxy-zoo-lofar">https://www.zooniverse.org/projects/chrismrp/radio-galaxy-zoo-lofar</a> </p> </div></div></div><div data-type="fulltextNote" id="fn2" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">b</sup> </span> <a class="uri" href="https://www.zooniverse.org/projects/hongming-tang/radio-galaxy-zoo-emu">https://www.zooniverse.org/projects/hongming-tang/radio-galaxy-zoo-emu</a> </p> </div></div></div><div data-type="fulltextNote" id="fn3" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">c</sup> </span> The observed metric differences between BYOL and SimCLR pre-trained models are not significant (below 1%) given the reported uncertainties.</p> </div></div></div><div data-type="fulltextNote" id="fn4" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">d</sup> </span> Out of <span data-mathjax-status="alt-graphic" class="inline-formula"> <span class="alternatives"> <img data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline35.png?pub-status=live" class="aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off" width="12" height="4" data-original-image="/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline35.png" data-zoomable="false" /> <span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on"> $\sim$ </span></span> </span> </span>5 800 catalogued sources that were labelled as candidate radio galaxies on the basis of their radio morphology, only one was found to have a size (7.4’) larger than the chosen image cutout (6.4’).</p> </div></div></div><div data-type="fulltextNote" id="fn5" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">e</sup> </span> Wide-angle tail</p> </div></div></div><div data-type="fulltextNote" id="fn6" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">f</sup> </span> narrow-angle tail</p> </div></div></div><div data-type="fulltextNote" id="fn7" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">g</sup> </span> The RGZ project is a crowdsourced science project where both scientists and citizens can classify radio galaxies and their host galaxies from radio and infrared (WISE survey, Wright et al. <a class="xref bibr" href="#ref57"><span class="show-for-sr">Reference Wright</span>2010</a>) images presented to users in a web interface</p> </div></div></div><div data-type="fulltextNote" id="fn8" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">h</sup> </span> When mentioning the <span class="monospace">ImageNet</span> dataset throughout the paper, we refer to the <span class="monospace">ImageNet-1k</span> version.</p> </div></div></div><div data-type="fulltextNote" id="fn9" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">i</sup> </span> <a class="uri" href="https://github.com/SKA-INAF/caesar-mrcnn-tf2">https://github.com/SKA-INAF/caesar-mrcnn-tf2</a> </p> </div></div></div><div data-type="fulltextNote" id="fn10" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">j</sup> </span> In astronomical source catalogue works, the recall/precision metrics are often referred to as completeness/reliability.</p> </div></div></div><div data-type="fulltextNote" id="fn11" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">k</sup> </span> LightGBM is a high-performance gradient boosting framework based on decision tree algorithm, particularly suited for classification tasks on tabular data. More details are available at <a class="uri" href="https://lightgbm.readthedocs.io/en/latest/index.html">https://lightgbm.readthedocs.io/en/latest/index.html</a>.</p> </div></div></div><div data-type="fulltextNote" id="fn12" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">l</sup> </span> <em class="italic">Isolation Forest</em> is an unsupervised decision-tree-based algorithm for outlier detection in tabular data, that works by randomly selecting a feature and a random split value to isolate data points in a binary tree. It identifies outliers as instances that require fewer splits to be isolated, exploiting the inherent rarity of anomalies in a dataset.</p> </div></div></div><div data-type="fulltextNote" id="fn13" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">m</sup> </span> <a class="uri" href="https://github.com/MichelleLochner/astronomaly">https://github.com/MichelleLochner/astronomaly</a> </p> </div></div></div><div data-type="fulltextNote" id="fn14" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">n</sup> </span> <a class="uri" href="https://github.com/SKA-INAF/caesar-rest">https://github.com/SKA-INAF/caesar-rest</a> </p> </div></div></div><div data-type="fulltextNote" id="fn15" class="circle-list__item"> <div class="circle-list__item__indicator"></div> <div class="circle-list__item__grouped"><div class="circle-list__item__grouped__content"> <p class="p"><span class="label"> <sup class="sup">o</sup> </span> <a class="uri" href="https://www.gnu.org/licenses/gpl-3.0.html">https://www.gnu.org/licenses/gpl-3.0.html</a> </p> </div></div></div></div> <hr aria-hidden="true" class="list-divider separator default" data-v-7036083a> <div id="references-list" class="circle-list"><h2>References</h2> <div id="ref1" aria-flowto="reference-1-content reference-1-button" class="circle-list__item"> <div class="circle-list__item__indicator"><AppButton icon="up-circle" aria-label="Return to the reference 1 in the content" id="reference-1-button" class="circle-list__item__indicator__up"></AppButton></div> <div aria-hidden="true" data-test-hidden="true" class="circle-list__item__number"> </div> <div class="circle-list__item__grouped"><div id="reference-1-content" class="circle-list__item__grouped__content"><span class="string-name"><span class="surname">Aniyan</span>, <span class="given-names">A. 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The number of images <span class="alternatives"><img class="inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off" data-mimesubtype="png" data-type="" src="${staticDomain}/content/id/urn:cambridge.org:id:article:S1323358024000845/resource/name/S1323358024000845_inline47.png?pub-status=live" /><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$n_{img}$</span></span></span> is reported in column (2). The image size <span class="alternatives"><img class="inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off" data-mimesubtype="png" data-type="" src="${staticDomain}/content/id/urn:cambridge.org:id:article:S1323358024000845/resource/name/S1323358024000845_inline48.png?pub-status=live" /><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$s_{img}$</span></span></span> is reported in column (3). <span class="alternatives"><img class="inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off" data-mimesubtype="png" data-type="" src="${staticDomain}/content/id/urn:cambridge.org:id:article:S1323358024000845/resource/name/S1323358024000845_inline49.png?pub-status=live" /><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$s_{img}$</span></span></span> is fixed for all images in the <span class="monospace">hulk_smgp</span> and <span class="monospace">hulk_emupilot</span> datasets, while <span class="alternatives"><img class="inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off" data-mimesubtype="png" data-type="" src="${staticDomain}/content/id/urn:cambridge.org:id:article:S1323358024000845/resource/name/S1323358024000845_inline50.png?pub-status=live" /><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$s_{img}$</span></span></span> is not fixed and depends on the source size <span class="alternatives"><img class="inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off" data-mimesubtype="png" data-type="" src="${staticDomain}/content/id/urn:cambridge.org:id:article:S1323358024000845/resource/name/S1323358024000845_inline51.png?pub-status=live" /><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$s_{\text{source}}$</span></span></span> (equivalent to the maximum source bounding box dimension) in the <span class="monospace">banner_smgps</span> and <span class="monospace">banner_emupilot</span> datasets. For these datasets, we report the average, minimum and maximum source sizes in columns (4), (5) and (6), respectively. Images from all datasets are eventually resized to a fixed size for model training and testing (see Section 2.3).</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 2" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-65434-mediumThumb-png-S1323358024000845_fig2.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-82944-optimisedImage-png-S1323358024000845_fig2.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 2.</span> <span data-v-241a4b23><span class="p">Representative examples of images from the <span class="monospace">hulk_smgps</span> (top panels), <span class="monospace">banner_smgps</span> (middle panels) and <span class="monospace">hulk_emupilot</span> (bottom panels) datasets. A zscale transform was applied to all images for visualization scopes. Top panels: sample images containing only compact sources (Figure 2(a)), or multiple extended sources (Figures 2(b) and 2(c)). Middle panels: sample source with diffuse morphology (Figure 2(d)), a multi-component extended source exhibiting typical radio galaxy morphology (Figure 2(e)), a single-component extended source with a roundish morphology (Figure 2(f)). Bottom panels: sample sources with FR-I (Figure 2(g)), FR-II (Figure 2(h)) and peculiar (Figure 2(i)) classification.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 3" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab2.png" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab2.png" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Table 2.</span> <span data-v-241a4b23><span class="p">List of augmentations used in SimCLR model training. In column (2) we reported the transform parameter values. In column (3) we reported the probability used to apply the transform in the augmentation pipeline, e.g. 1.0 means the transform is always applied to all input images.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 4" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab3.png" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab3.png" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Table 3.</span> <span data-v-241a4b23><span class="p">List of hyperparameters used in SimCLR model training.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 5" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-89259-mediumThumb-png-S1323358024000845_fig3.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-13619-optimisedImage-png-S1323358024000845_fig3.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 3.</span> <span data-v-241a4b23><span class="p">Sample images from the RGZ dataset with representative sources of different morphological classes (reported below each frame). A zscale transform was applied to all images for visualization scopes.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 6" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-73742-mediumThumb-png-S1323358024000845_fig4.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-30709-optimisedImage-png-S1323358024000845_fig4.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 4.</span> <span data-v-241a4b23><span class="p">2D UMAP projection of the data representation vector (size = 512) produced by the trained <span class="monospace">smart_hulk_smgps</span> model on the RGZ dataset.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 7" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-68307-mediumThumb-png-S1323358024000845_fig5.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-95705-optimisedImage-png-S1323358024000845_fig5.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 5.</span> <span data-v-241a4b23><span class="p">Classification F1-scores obtained for different classes and for all classes cumulatively over RGZ test sets with different pre-trained and frozen backbone models: <span class="monospace">hulk_smgps</span> (red squares), <span class="monospace">banner_smgps</span> (blue inverted triangles), <span class="monospace">smart_hulk_smgps</span> (green triangles), <span class="monospace">hulk_emupilot</span> (orange diamonds), <span class="monospace">banner_emupilot</span> (cyan asterisks), <span class="monospace">ImageNet</span> (black dots). The reported values and errors are the F1-score mean and mean error computed over five test sets.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 8" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-17641-mediumThumb-png-S1323358024000845_fig6.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-01879-optimisedImage-png-S1323358024000845_fig6.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 6.</span> <span data-v-241a4b23><span class="p">Confusion matrix of the source morphology classifier (trained with <span class="monospace">smart_hulk_smgps</span> pre-trained and frozen backbone model) obtained over the RGZ test set.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 9" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-63009-mediumThumb-png-S1323358024000845_fig7.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-99012-optimisedImage-png-S1323358024000845_fig7.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 7.</span> <span data-v-241a4b23><span class="p">Classification F1-scores obtained (for all classes cumulatively) over RGZ test sets as a function of the number of images <span class="alternatives"><img class="inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off" data-mimesubtype="png" data-type="" src="${staticDomain}/content/id/urn:cambridge.org:id:article:S1323358024000845/resource/name/S1323358024000845_inline85.png?pub-status=live" /><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$n_{train}$</span></span></span> in the training set with two alternative models: one trained from scratch (open black dots), the other trained with backbone model weights initialized to <span class="monospace">smart_hulk_smgps</span> weights (filled black dots). The upper x-axis indicates the fraction of the full training set considered in each training run.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 10" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-87738-mediumThumb-png-S1323358024000845_fig8.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-36452-optimisedImage-png-S1323358024000845_fig8.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 8.</span> <span data-v-241a4b23><span class="p">Sample images (taken from Riggi 2023) from the dataset used for <span class="italic">caesar-mrcnn</span> training/testing, including objects of different classes: a <span class="monospace">FLAGGED</span> object (Figure 8(a), in gray), <span class="monospace">COMPACT</span> objects (in blue), a <span class="monospace">MULTI-ISLAND</span> object (Figure 8(b), in orange), <span class="monospace">EXTENDED</span> objects (Figure 8(c), in yellow), <span class="monospace">SPURIOUS</span> objects (Figure 8(d), in red).</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 11" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-16536-mediumThumb-png-S1323358024000845_fig9.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-90428-optimisedImage-png-S1323358024000845_fig9.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 9.</span> <span data-v-241a4b23><span class="p">Mask R-CNN object detection F1-score metric obtained for different object classes over multiple test sets with different pre-trained and frozen backbone models: <span class="monospace">hulk_smgps</span> (red squares), <span class="monospace">banner_smgps</span> (blue iverted triangles), <span class="monospace">smart_hulk_smgps</span> (green triangles), <span class="monospace">hulk_emupilot</span> (orange diamonds), <span class="monospace">banner_emupilot</span> (cyan asterisks), <span class="monospace">ImageNet</span> (black dots). The reported values and errors are the means and mean errors computed over 5 test sets.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 12" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-69728-mediumThumb-png-S1323358024000845_fig10.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-97907-optimisedImage-png-S1323358024000845_fig10.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 10.</span> <span data-v-241a4b23><span class="p">Mask R-CNN object detection F1-score metric obtained over the <span class="monospace">SOURCE</span> class over multiple test sets as a function of the number of images <span class="alternatives"><img class="inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off" data-mimesubtype="png" data-type="" src="${staticDomain}/content/id/urn:cambridge.org:id:article:S1323358024000845/resource/name/S1323358024000845_inline87.png?pub-status=live" /><span class="mathjax-tex-wrapper" data-mathjax-type="texmath"><span class="tex-math mathjax-tex-math mathjax-on">$n_{train}$</span></span></span> in the training set with two alternative models: one trained from scratch (open markers), the other trained with backbone model weights initialized to <span class="monospace">hulk_smgps</span> weights (filled markers). The upper x-axis indicates the fraction of the full training set considered in each training run.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 13" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-69911-mediumThumb-png-S1323358024000845_fig11.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-74419-optimisedImage-png-S1323358024000845_fig11.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 11.</span> <span data-v-241a4b23><span class="p">Sample images from the <span class="monospace">hulk_emupilot</span> dataset, labelled as <span class="monospace">PECULIAR</span> and <span class="monospace">COMPACT</span>. The other assigned labels are reported below each frame. A zscale transform was applied to all images for visualization scopes.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 14" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-37535-mediumThumb-png-S1323358024000845_fig12.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-03853-optimisedImage-png-S1323358024000845_fig12.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure 12.</span> <span data-v-241a4b23><span class="p">Left: Anomaly score of frames contained in the <span class="monospace">hulk_emupilot</span> dataset, shown as black solid histogram, found with the <span class="italic">Isolation Forest</span> algorithm over top-10 feature data. Unclassified frames are shown with a dashed line. Red filled histogram are the scores of peculiar frames. Ordinary frames (e.g. hosting only compact or artefacts) are shown in blue, pure compact frames in light blue, while frames not tagged as peculiar that host complex sources or structures (<span class="monospace">EXTENDED</span>, <span class="monospace">DIFFUSE</span>, <span class="monospace">DIFFUSE-LARGE</span>, <span class="monospace">RADIO-GALAXY</span>) are shown in green. Right: Anomaly detection metrics (recall, precision, contamination) as a function of the applied anomaly score threshold. Red solid and dashed lines indicate the recall and precision achieved on peculiar frame detection. Purple dotted line is the precision obtained over both peculiar and complex frames. The other solid coloured lines indicate the fraction of unclassified (black line), complex (green line) and ordinary frames contaminating the selected anomaly sample.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 15" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab4.png" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab4.png" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Table 4.</span> <span data-v-241a4b23><span class="p">Peculiar frame detection metrics obtained with the <span class="italic">Isolation Forest</span> algorithm over selected feature sets (column (1)) when using an anomaly score threshold (reported in column (2)) that provides the best compromise in terms of peculiar frame recall and precision, respectively shown in columns (3) and (4). The precision relative to joint peculiar and complex frames is shown in column (5). The fractions of complex and ordinary frames contaminating the predicted anomalous sample are shown in columns (6) and (7).</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 16" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-02897-mediumThumb-png-S1323358024000845_fig13.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-59184-optimisedImage-png-S1323358024000845_fig13.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure A.1.</span> <span data-v-241a4b23><span class="p">Examples of sources from the RGZ test dataset that were misclassified by the trained source classifier (<span class="monospace">hulk_smgps</span> pre-trained and frozen backbone model) due to an incorrect true class label provided in the dataset (mislabelling). The true and predicted class labels are reported below each frame. In many cases, the model indeed correctly predicted the expected true classification (denoted as “true corr.” below each frame).</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 17" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig14.png" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig14.png" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure A.2.</span> <span data-v-241a4b23><span class="p">Feature importance obtained with a LightGBM classifier trained on <span class="monospace">hulk_emupilot</span> data representation, for the classification of interesting against ordinary images.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 18" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-70422-mediumThumb-png-S1323358024000845_fig15.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-11677-optimisedImage-png-S1323358024000845_fig15.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure A.3.</span> <span data-v-241a4b23><span class="p">Figure 14: 2D UMAP projection of the top-15 selected features from the data representation vector produced by the trained SimCLR model on the <span class="monospace">hulk_emupilot</span> dataset as a function of the image noise RMS level in logarithmic scale (z-scale axis). Red markers correspond to image with higher RMS levels, while blue markers to low noise RMS levels. Left: 2D UMAP projection of the top-15 selected features for unclassified frames (gray markers) and labelled frames (coloured markers, as reported in the plot legends). See text for details on label schema.</span></span></p></div> </div></div> <hr aria-hidden="true" class="separator dashed" data-v-7036083a data-v-241a4b23></div><div data-v-241a4b23><div class="figures__item" data-v-241a4b23><div class="figures__item__image-box" data-v-241a4b23><button class="figures__ref" data-v-241a4b23> View in content </button> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==" alt="Figure 19" data-zoomable="true" data-src="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-44984-mediumThumb-png-S1323358024000845_fig16.jpg" data-enlarged-image="https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary-alt:20241104171006-37754-optimisedImage-png-S1323358024000845_fig16.jpg" class="graphic" data-v-241a4b23></div> <div data-v-241a4b23><div class="caption" data-v-241a4b23><p data-v-241a4b23><span class="label" data-v-241a4b23>Figure A.4.</span> <span data-v-241a4b23><span class="p">Screenshot of <span class="monospace">astronomaly</span> web UI with list of anomalous frames selected from the <span class="monospace">hulk_emupilot</span> dataset.</span></span></p></div> </div></div> </div></div>         <div id="metrics-tab" publication-date="05 November 2024" class="metrics tab-pane" data-v-c41a0c86><div class="app-loader" data-v-c41a0c86></div></div></div></div> </div> <div role="complementary" aria-label="related contents" class="column__main__right" data-v-01274b1d><div class="access-block row access-status" data-v-5fad35b8 data-v-01274b1d><span class="has-access" data-v-5fad35b8><img src="data:image/svg+xml;base64,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" alt="" class="app-icon access" data-v-d2c09870 data-v-5fad35b8> <span class="sr-only" data-v-5fad35b8>You have </span> Access </span> </div>    </div></div></div></div></div> <div id="cited-by-modal" role="dialog" aria-labelledby="Cited by modal" aria-hidden="true" class="modal fade" data-v-014d05be data-v-01274b1d><div class="modal-dialog modal-xl cited-by-modal" data-v-014d05be><div tabindex="-1" class="modal-content" data-v-014d05be><div class="modal-header" data-v-014d05be><h1 class="modal-header__heading" data-v-014d05be>Cited by</h1></div> <div class="modal-body" data-v-014d05be><div class="modal-body__loader" data-v-014d05be><div class="modal-body__loader__spinner" data-v-014d05be></div> <p class="modal-body__loader__message" data-v-014d05be>Loading...</p></div></div> <button aria-label="Close Cited by" aria-expanded="false" data-dismiss="modal" class="app-button cited-by-modal__button--close app-button__icon app-button--" data-v-2a038744 data-v-014d05be><img src="data:image/svg+xml;base64,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" alt="" class="app-icon icon close-modal" data-v-d2c09870 data-v-2a038744> </button></div></div></div></div></div></div></div><script>window.__NUXT__=(function(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y){return {layout:"default",data:[{article:{id:"E4F61E099F4092E9229652B4BB68DD41",metadata:{title:v,htmlTitle:v,subtitle:a,authorsGroup:{authors:{contributors:[{givenNames:w,surname:"Riggi",nameStyle:d,affiliations:[{text:h}],isCorresponding:c,notes:"\u003Cdiv class=\"corresp\"\u003E\u003Cspan class=\"bold\"\u003ECorresponding author:\u003C\u002Fspan\u003E S. 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Published by Cambridge University Press on behalf of Astronomical Society of Australia"],holder:["The Author(s)"],year:[2024]},creativeCommons:d,acceptedManuscript:b,type:"research-article",typeDescription:"Research Article",eNumber:"e085",commentsCount:z,topicsAndSubtopics:d},journal:{id:D,title:p,titleSlug:E,mnemonic:"PAS",titleHistory:[],isFirstView:b,journalSlug:E,isCompanion:b,parentCompanionJournalName:p,associatedParentCollection:d,paymentInfo:{prices:{"£":{price:26,sku:q,skuNew:n,currency:"£"},"€":{price:31,sku:q,skuNew:n,currency:"€"},US$:{price:36,sku:q,skuNew:n,currency:"US$"},AU$:{price:51,sku:q,skuNew:n,currency:"AU$"}}},url:F,firstViewUrl:"\u002Fcore\u002Fjournals\u002Fpublications-of-the-astronomical-society-of-australia\u002Ffirstview",coverUrl:"https:\u002F\u002Fstatic.cambridge.org\u002Fcovers\u002FPAS_0_0_0\u002Fpublications-of-the-astronomical-society-of-australia.jpg",submitMaterialsUrl:"\u002Fcore\u002Fjournals\u002Fpublications-of-the-astronomical-society-of-australia\u002Finformation\u002Fauthor-instructions\u002Fsubmitting-your-materials",hasHistory:b,latestTitle:p,latestId:D,hasPastTitle:b,volume:{id:"41F60CAF610317F3B352E354D356E178",number:"41",title:G,publishedDate:j,printPublishTimestamp:1704067200000,url:H}},abstract:{textAbstracts:[{title:"Abstract",content:"\u003Cdiv class=\"abstract\" data-abstract-type=\"normal\"\u003E\u003Cp\u003ENew advancements in radio data post-processing are underway within the Square Kilometre Array (SKA) precursor community, aiming to facilitate the extraction of scientific results from survey images through a semi-automated approach. Several of these developments leverage deep learning methodologies for diverse tasks, including source detection, object or morphology classification, and anomaly detection. Despite substantial progress, the full potential of these methods often remains untapped due to challenges associated with training large supervised models, particularly in the presence of small and class-unbalanced labelled datasets.\u003C\u002Fp\u003E\u003Cp\u003ESelf-supervised learning has recently established itself as a powerful methodology to deal with some of the aforementioned challenges, by directly learning a lower-dimensional representation from large samples of unlabelled data. The resulting model and data representation can then be used for data inspection and various downstream tasks if a small subset of labelled data is available.\u003C\u002Fp\u003E\u003Cp\u003EIn this work, we explored contrastive learning methods to learn suitable radio data representations by training the SimCLR model on large collections of unlabelled radio images taken from the ASKAP EMU and SARAO MeerKAT GPS surveys. The resulting models were fine-tuned over smaller labelled datasets, including annotated images from various radio surveys, and evaluated on radio source detection and classification tasks. Additionally, we employed the trained self-supervised models to extract features from radio images, which were used in an unsupervised search for objects with peculiar morphology in the ASKAP EMU pilot survey data. For all considered downstream tasks, we reported the model performance metrics and discussed the benefits brought by self-supervised pre-training, paving the way for building radio foundational models in the SKA era.\u003C\u002Fp\u003E\u003C\u002Fdiv\u003E",lang:I}]},content:{html:"\u003Cdiv class=\"article research-article NLM\"\u003E\n\n\u003Cdiv class=\"body\"\u003E\n\u003Cdiv class=\"sec intro\" data-magellan-destination=\"s1\" id=\"s1\"\u003E\n\n\u003Ch2 class=\"A\"\u003E\u003Cspan class=\"label\"\u003E1.\u003C\u002Fspan\u003E Introduction\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E Radio astronomy stands at the threshold of a transformative era, marked by the advent of large sky surveys carried out with instruments such as the Square Kilometre Array (SKA) (Dewdney et al., \u003Ca class=\"xref bibr\" href=\"#ref12\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Dewdney\u003C\u002Fspan\u003E2016\u003C\u002Fa\u003E) and its precursor telescopes. As the field enters this golden age, the immense volumes of observational data generated pose unprecedented challenges and opportunities. For example, the Evolutionary Map of the Universe (EMU) (Norris et al., \u003Ca class=\"xref bibr\" href=\"#ref40\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Norris\u003C\u002Fspan\u003E2011\u003C\u002Fa\u003E) of the Australian SKA Pathfinder (ASKAP, Johnston et al., \u003Ca class=\"xref bibr\" href=\"#ref24\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Johnston\u003C\u002Fspan\u003E2008\u003C\u002Fa\u003E; Hotan et al., \u003Ca class=\"xref bibr\" href=\"#ref22\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Hotan\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) started in 2022 to survey \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline1.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline1.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E75% of the sky at 940 MHz with an angular resolution of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline2.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline2.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E15\u003Csup class=\"sup\"\u003E′′\u003C\u002Fsup\u003E and a noise rms of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline3.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline3.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E15 \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline4.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"11\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline4.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mu$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003EJy\u002Fbeam. The EMU source cataloguing process will require an unprecedented degree of automation and knowledge extraction, as the expected number of detectable sources is \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline5.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline5.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E50 millions. So will be for other precursors and future SKA observations. The sheer scale and complexity of these datasets demand innovative approaches to shorten the time needed to deliver scientific results or groundbreaking discoveries.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In this context, machine learning (ML) emerges as a powerful tool for unlocking the full potential of radio astronomy data, offering solutions to complex tasks that are often beyond the reach of conventional methods in multiple areas, including source extraction, classification (e.g. morphological or astrophysical type) and discovery of anomalous\u002Funexpected objects. Most existing contributions focused on galaxy morphology classification for extragalactic science cases employing either supervised learning (SL), e.g. with convolutional neural networks (CNNs) (Aniyan & Thorat \u003Ca class=\"xref bibr\" href=\"#ref1\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Aniyan and Thorat\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E; Lukic et al., \u003Ca class=\"xref bibr\" href=\"#ref33\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lukic\u003C\u002Fspan\u003E2018\u003C\u002Fa\u003E; Wu et al., \u003Ca class=\"xref bibr\" href=\"#ref58\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Wu\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E; Lao et al., \u003Ca class=\"xref bibr\" href=\"#ref28\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lao\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) or Vision Transformers (ViTs) (Gupta et al., \u003Ca class=\"xref bibr\" href=\"#ref17\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E), weakly-supervised learning (Gupta et al., \u003Ca class=\"xref bibr\" href=\"#ref18\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E), semi-supervised learning (Slijepcevic et al., \u003Ca class=\"xref bibr\" href=\"#ref49\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Slijepcevic\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E), or unsupervised learning, e.g. Self-Organizing Maps (SOMs) (Galvin et al., \u003Ca class=\"xref bibr\" href=\"#ref13\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Galvin\u003C\u002Fspan\u003E2020\u003C\u002Fa\u003E; Mostert et al., \u003Ca class=\"xref bibr\" href=\"#ref37\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Mostert\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E; Gupta et al., \u003Ca class=\"xref bibr\" href=\"#ref19\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E) or t-distributed stochastic neighbour embedding (Pennock et al., \u003Ca class=\"xref bibr\" href=\"#ref43\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Pennock\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Despite substantial progress, the full potential of supervised approaches often remains untapped due to the scarcity of large and high-quality annotated radio image datasets, crucial for training very deep models. The human effort required to produce them is in fact unsustainable. Citizen science projects, launched within different precursor surveys on the Zooniverse platform\u003Ca class=\"xref fn\" href=\"#fn1\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ea\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E\n\u003Csup class=\"sup\"\u003E,\u003C\u002Fsup\u003E \n\u003Ca class=\"xref fn\" href=\"#fn2\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Eb\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E and building on the previous Radio Galaxy Zoo project (Banfield et al., \u003Ca class=\"xref bibr\" href=\"#ref2\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Banfield\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E), will partially alleviate this need, at the cost of potentially introducing errors and biases in the cumulative dataset. As a result, existing labelled radio datasets are typically very limited in size, class-unbalanced, and adopt a diverse or ambiguous labelling schema, usually depending on the particular domain of application. Several applications produced so far for either radio source classification or source detection scopes, have therefore resorted to fine-tune models that were previously pre-trained on large annotated collections of non-astronomical data, such as the \u003Cem class=\"italic\"\u003EImageNet\u003C\u002Fem\u003E (Deng et al., \u003Ca class=\"xref bibr\" href=\"#ref11\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Deng\u003C\u002Fspan\u003E2009\u003C\u002Fa\u003E) or \u003Cem class=\"italic\"\u003ECOCO\u003C\u002Fem\u003E (Tsung-Yi et al., \u003Ca class=\"xref bibr\" href=\"#ref53\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Tsung-Yi\u003C\u002Fspan\u003E2014\u003C\u002Fa\u003E) datasets, that may not well capture all distinctive features of radio observations. On the other hand, completely unsupervised approaches are not very effective when directly dealing with highly dimensional image data, typically requiring previous feature extraction and dimensionality reduction steps to be applied. Currently, employed methods based on SOMs typically enforce an apriori discrete static data organization that do not well support extension to new tasks. These limitations necessitate exploring alternative methodologies.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Representation learning (Bengio & Anal \u003Ca class=\"xref bibr\" href=\"#ref4\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Bengio and Anal\u003C\u002Fspan\u003E2013\u003C\u002Fa\u003E), and in particular self-supervised learning (SSL) (Liu et al., \u003Ca class=\"xref bibr\" href=\"#ref32\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Liu\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E), has recently emerged as a promising avenue to address these issues, by directly learning (pretext task), without any supervision, a lower-dimensionality representation (i.e. the latent space) from large samples of unlabelled data. The resulting model and data representation can then be used for data inspection and generalized for various applications (downstream tasks), e.g. classification, object detection, etc, if a small subset of labelled data is available. Previous works in the radio domain are based on convolutional autoencoders (CAE) generative methods, which learns a latent space by minimizing a loss between input data and data reconstructed through an encoder-decoder network. For example, Ralph et al. \u003Ca class=\"xref bibr\" href=\"#ref45\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Ralph\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E developed a pipeline for unsupervised source morphology studies based on SOMs and k-mean clustering algorithm, employing CAEs to extract features from the Radio Galaxy Zoo (RGZ) (Banfield et al., \u003Ca class=\"xref bibr\" href=\"#ref2\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Banfield\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E) images. Bordiu et al. (\u003Ca class=\"xref bibr\" href=\"#ref7\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Bordiu\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) employed CAEs to extract features from combined radio and infrared images of known Galactic supernova remnants (SNRs) to search for possible multiwavelength patterns.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Contrastive learning approaches, on the other hand, employ siamese or teacher-student network architectures, minimizing the similarity between augmented versions of the input data, eventually in contrast to negative samples. They were reported to obtain superior performance on natural images in classification tasks (e.g. rivalling supervised methods), quality of representation learnt, computation efficiency, and robustness to noise. Recently, Slijepcevic et al. (\u003Ca class=\"xref bibr\" href=\"#ref50\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Slijepcevic\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E) trained BYOL (Grill et al., \u003Ca class=\"xref bibr\" href=\"#ref15\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Grill\u003C\u002Fspan\u003E2020\u003C\u002Fa\u003E) contrastive learning method over a sample of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline6.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline6.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E10\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline7.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"5\" height=\"7\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline7.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$^{5}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E radio source RGZ images from the VLA FIRST survey (Becker et al., \u003Ca class=\"xref bibr\" href=\"#ref3\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Becker\u003C\u002Fspan\u003E1995\u003C\u002Fa\u003E). The resulting self-supervised model was then fine-tuned to classify FRI\u002FFRII radio galaxies from the VLA FIRST survey, as listed in the \u003Cem class=\"italic\"\u003EMirabest\u003C\u002Fem\u003E dataset (Porter & Scaife \u003Ca class=\"xref bibr\" href=\"#ref44\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Porter and Scaife\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E). The analysis was repeated over a second dataset that include data from the MeerKAT MIGHTEE survey. Both analyses indicated an increase in classification accuracy (ranging from few percent to 8% for MIGHTEE) over the same model trained in a completely supervised way. Mohale & Lochner (\u003Ca class=\"xref bibr\" href=\"#ref36\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Mohale and Lochner\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E) carried out a similar FRI\u002FFRII classification analysis over the \u003Cem class=\"italic\"\u003EMirabest\u003C\u002Fem\u003E dataset, using self-supervised models, previously pre-trained over the \u003Cem class=\"italic\"\u003EImageNet-1k\u003C\u002Fem\u003E (natural images), RGZ (radio galaxy images), Galaxy Zoo DECaLS (optical galaxy images) datasets. Using a KNN classifier evaluation, they found that the model pre-trained on RGZ outperforms the others by a considerable margin (5% to 10% improvement in accuracy). Hossain et al. (\u003Ca class=\"xref bibr\" href=\"#ref21\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Hossain\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) carried out the same analysis with both BYOL and SimCLR (Chen et al., 2020) self-supervised models but using Group Equivariant Convolutional Neural Network (G-CNN) backbones to make models invariant to different isometries (translation, rotation, mirror reflection). They pre-trained self-supervised models on the RGZ dataset and fine-tuned them on \u003Cem class=\"italic\"\u003EMirabest\u003C\u002Fem\u003E dataset, obtaining FRI\u002FFRII classification accuracies around 95%-97%\u003Ca class=\"xref fn\" href=\"#fn3\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ec\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E, improving by \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline8.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline8.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E2% the fully supervised baseline.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E With respect to previous studies, we focused more on SKA precursor data, training the SimCLR self-supervised model over large samples of unlabelled images, extracted from ASKAP and MeerKAT radio maps in two different modes: (1) “source-centered” mode, e.g. images centred and zoomed over catalogued sources (as in previous studies); (2) “blind” or “random” mode, e.g. images with arbitrary fixed size extracted from the entire map, without any source position awareness. The backbone component of the trained self-supervised models, a \u003Cem class=\"italic\"\u003EResNet18\u003C\u002Fem\u003E neural network, was then evaluated and fine-tuned on labelled datasets to solve two representative radio source analysis tasks: radio source morphology classification and radio source instance segmentation. Additionally, the backbone model was used as a feature extractor for radio images, enabling an unsupervised search for radio objects with peculiar morphology based on the extracted data representation. Compared to previous studies, we assessed the trained models over larger labelled datasets, comprising thousands of annotated images from various radio surveys (VLA FIRST, ASKAP pilot, ATCA Scorpio), that were not previously used for self-supervised model pre-training. This study aims to quantify the benefits of self-supervision for the radio domain, providing ready-to-use foundational models that can be exploited in SKA precursor or other radio surveys as feature extractors for similar analysis or to tackle completely new tasks.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f1\" id=\"f1\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig1.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"5177\" height=\"2445\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig1.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 1.\u003C\u002Fspan\u003E Schema of self-supervised learning for radio data analysis.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E The paper is organized as follows. In \u003Ca class=\"xref sec\" href=\"#s2\"\u003ESection 2\u003C\u002Fa\u003E we describe the contrastive learning model considered, along with the training datasets, data pre-processing and training methodologies adopted. In \u003Ca class=\"xref sec\" href=\"#s3\"\u003ESections 3\u003C\u002Fa\u003E, \u003Ca class=\"xref sec\" href=\"#s4\"\u003E4\u003C\u002Fa\u003E, and \u003Ca class=\"xref sec\" href=\"#s5\"\u003E5\u003C\u002Fa\u003E we studied how the trained self-supervised models perform in the three selected analysis scenarios, reporting performances achieved against benchmark supervised models. Finally, in \u003Ca class=\"xref sec\" href=\"#s6\"\u003ESection 6\u003C\u002Fa\u003E we summarize the obtained results and discuss future steps.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec other\" data-magellan-destination=\"s2\" id=\"s2\"\u003E\n\n\u003Ch2 class=\"A\"\u003E\u003Cspan class=\"label\"\u003E2.\u003C\u002Fspan\u003E Self-supervised learning of radio data\u003C\u002Fh2\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s2-1\" id=\"s2-1\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E2.1\u003C\u002Fspan\u003E Contrastive learning model\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E \n\u003Ca class=\"xref fig\" href=\"#f1\"\u003EFigure 1\u003C\u002Fa\u003E illustrates how self-supervised learning can be used for radio data analysis. Initially, a self-supervised framework (indicated by the red block) is trained on large samples of unlabelled image data. Subsequently, the resulting model backbone and data representation (or latent space vector) can be utilized for various downstream tasks, such as data inspection or anomaly detection, typically employing dimensionality reduction methods. Furthermore, the model can be applied to source detection and classification analysis using new labelled datasets. In this study, we used \u003Cem class=\"italic\"\u003ESimCLR\u003C\u002Fem\u003E as the self-supervised framework for our analysis.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E SimCLR (Chen et al., 2020) is a simple yet widely used popular self-supervised learning framework. It learns data representations by maximizing the similarity between augmented views of the same input data (\u003Cem class=\"italic\"\u003Epositive examples\u003C\u002Fem\u003E) relative to augmented views of different input data within the same training batch (\u003Cem class=\"italic\"\u003Enegative examples\u003C\u002Fem\u003E). The architecture of SimCLR, depicted in \u003Ca class=\"xref fig\" href=\"#f1\"\u003EFigure 1\u003C\u002Fa\u003E, consists of two main components: a base encoder network \u003Cem class=\"italic\"\u003Ef\u003C\u002Fem\u003E, which is typically a \u003Cem class=\"italic\"\u003EResNet\u003C\u002Fem\u003E network (He et al., \u003Ca class=\"xref bibr\" href=\"#ref20\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference He\u003C\u002Fspan\u003E2016\u003C\u002Fa\u003E), and a small projection head network \u003Cem class=\"italic\"\u003Eg\u003C\u002Fem\u003E, which is typically a Multi-Layer Perceptron (MLP) with one or two layers. Input images \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline9.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"13\" height=\"9\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline9.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathbf{x}_{k}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E (\u003Cem class=\"italic\"\u003Ek\u003C\u002Fem\u003E = 1,...,N) in a given batch sample of size \u003Cem class=\"italic\"\u003EN\u003C\u002Fem\u003E are first processed to produce two augmented views (or positive pair) \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline10.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"30\" height=\"14\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline10.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\hat{\\mathbf{x}}_{2k-1}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline11.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"18\" height=\"14\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline11.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\hat{\\mathbf{x}}_{2k}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E, by randomly applying multiple transformations from a specified transform set \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline12.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"13\" height=\"12\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline12.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathcal{T}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E. The encoder network, also denoted as the \u003Cem class=\"italic\"\u003Ebackbone model\u003C\u002Fem\u003E throughout the paper, extracts representation vectors \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline13.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"102\" height=\"16\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline13.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathbf{h}_{2k-1}= f(\\mathbf{x}_{2k-1})$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline14.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"74\" height=\"16\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline14.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathbf{h}_{2k}= f(\\mathbf{x}_{2k})$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E from each augmented data pair. The projector network maps the representations to a space where a contrastive loss is applied, obtaining vectors \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline15.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"102\" height=\"16\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline15.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathbf{z}_{2k-1}= g(\\mathbf{h}_{2k-1})$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline16.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"74\" height=\"16\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline16.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathbf{z}_{2k}= g(\\mathbf{h}_{2k})$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E. The contrastive loss \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline17.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"11\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline17.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathcal{L}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E, which is minimized during model training, is defined as: \u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\" data-magellan-destination=\"disp1\" id=\"disp1\"\u003E\n\u003Cspan class=\"label\"\u003E(1)\u003C\u002Fspan\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn1.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"192\" height=\"47\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn1.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n\\begin{align}\\mathcal{L} = \\frac{1}{2N}\\sum_{k=1}^{N}[l_{2k-1,2k} + l_{2k,2k-1}]\\end{align}\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\" data-magellan-destination=\"disp2\" id=\"disp2\"\u003E\n\u003Cspan class=\"label\"\u003E(2)\u003C\u002Fspan\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn2.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"255\" height=\"42\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn2.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n\\begin{align}l_{i,j} = -\\log{\\frac{\\exp\\!(\\text{sim}(\\mathbf{z}_{i},\\mathbf{z}_{j})\u002F\\tau)}{\\sum_{k=1}^{2N} \\unicode{x1D7D9}_{k\\neq i} \\exp\\!(\\text{sim}(\\mathbf{z}_{i},\\mathbf{z}_{k})\u002F\\tau)}}\\end{align}\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\u003Cp class=\"p continuation\"\u003Ewhere \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline18.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"16\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline18.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$l_{i,j}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E is the normalized temperature-scaled cross entropy loss (NT-Xent), \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline19.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"27\" height=\"17\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline19.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\unicode{x1D7D9}_{k \\neq i}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E = 1 if \u003Cem class=\"italic\"\u003Ek\u003C\u002Fem\u003E = \u003Cem class=\"italic\"\u003Ei\u003C\u002Fem\u003E (equal to 0 otherwise), \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline20.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"8\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline20.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\tau$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E is a temperature parameter, and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline21.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"62\" height=\"17\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline21.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\text{sim}(\\mathbf{z}_i,\\mathbf{z}_j)$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E is the pair-wise similarity between vectors \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline22.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"9\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline22.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathbf{z}_i$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline23.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"12\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline23.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathbf{z}_j$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E, defined as: \u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\" data-magellan-destination=\"disp3\" id=\"disp3\"\u003E\n\u003Cspan class=\"label\"\u003E(3)\u003C\u002Fspan\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn3.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"151\" height=\"42\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn3.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n\\begin{align}\\text{sim}(\\mathbf{z}_i,\\mathbf{z}_j)= \\frac{\\mathbf{z}_{i}^{T}\\mathbf{z}_j}{\\parallel\\mathbf{z}_i\\parallel\\;\\parallel\\mathbf{z}_j\\parallel }\\end{align}\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s2-2\" id=\"s2-2\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E2.2\u003C\u002Fspan\u003E Datasets\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E We created the following unlabelled datasets for training SimCLR:\u003C\u002Fp\u003E\u003Col class=\"list number nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E1.\u003C\u002Fspan\u003E Two distinct datasets were generated using data from the SARAO MeerKAT Galactic Plane Survey (SMGPS) (Goedhart et al., \u003Ca class=\"xref bibr\" href=\"#ref14\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Goedhart\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E), which covers a large portion of the 1st, 3rd and 4th Galactic quadrants (l = 2\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline24.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"5\" height=\"5\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline24.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$^{\\circ}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E−61\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline25.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"5\" height=\"5\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline25.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$^{\\circ}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E, 251\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline26.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"5\" height=\"5\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline26.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$^{\\circ}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E−358\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline27.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"5\" height=\"5\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline27.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$^{\\circ}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E, \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline28.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"29\" height=\"14\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline28.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$|b| \\lt $\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E1.5\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline29.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"5\" height=\"5\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline29.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$^{\\circ}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E) in the L-band (886–1 678 MHz). The survey has an angular resolution of 8\u003Csup class=\"sup\"\u003E′′\u003C\u002Fsup\u003E and a noise rms of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline30.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline30.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E10-20 \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline31.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"11\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline31.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mu$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003EJy\u002Fbeam at 1.3 GHz:\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E: A collection of 178,057 radio images, each of fixed size (256\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline32.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline32.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E256 pixels, equivalent to \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline33.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline33.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E6.4’\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline34.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline34.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E6.4’), extracted from SMGPS 1.28 GHz integrated intensity maps. This dataset was created by assuming a sliding window that traverses the entire surveyed area with a shift size equal to half the frame size, resulting in a 50% overlap among frames. The image size was chosen to be large enough to encompass the most extended radio galaxies that might be located in the cutout\u003Ca class=\"xref fn\" href=\"#fn4\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ed\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E: A collection of 17 062 radio images extracted from SMGPS 1.3 GHz integrated maps, each centered around sources listed in the SMGPS extended source catalogue (Bordiu et al., \u003Ca class=\"xref bibr\" href=\"#ref6\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Bordiu\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E). The size of the images varies across the dataset and is set to 1.5 times the size of the source bounding box. The radio sources in this dataset exhibit different morphologies, including single-island, multi-island, and diffuse sources.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E2.\u003C\u002Fspan\u003E Two distinct datasets were generated using data from the ASKAP EMU pilot survey (Norris et al., \u003Ca class=\"xref bibr\" href=\"#ref41\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Norris\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003Ea), which covered approximately 270 deg\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline36.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"5\" height=\"7\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline36.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$^{2}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E of the Dark Energy Survey area, achieving an angular resolution of 11\u003Csup class=\"sup\"\u003E′′\u003C\u002Fsup\u003E to 18\u003Csup class=\"sup\"\u003E′′\u003C\u002Fsup\u003E and a noise rms of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline37.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline37.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E30 \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline38.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"11\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline38.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mu$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003EJy\u002Fbeam at 944 MHz:\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E: A collection of 55 773 radio images, each of fixed size (256\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline39.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline39.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E256 pixels, equivalent to \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline40.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline40.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E8.5’\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline41.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline41.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E8.5’), extracted from ASKAP EMU pilot 944 MHz integrated map. The images were extracted using a sliding frame that traversed the entire mosaic with a shift size equal to half the frame size, resulting in a 50% overlap among frames.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E: A collection of 10,414 radio images extracted from ASKAP EMU pilot 944 MHz integrated map, each centered around extended sources listed in the pilot source catalogue compiled by Gupta et al. (\u003Ca class=\"xref bibr\" href=\"#ref17\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E). The size of the images varies across the dataset and is set to 1.5 times the size of the source bounding box. The radio sources in this dataset exhibit different morphologies, including FR-I (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline42.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline42.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E6%), FR-II (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline43.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline43.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E54%), FR-x (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline44.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline44.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E14%), single-peak resolved (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline45.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline45.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E23%) radio galaxies. \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline46.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline46.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E3% of the sources present a rare morphology not fitting into the previously mentioned categories.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Fol\u003E\n\n\u003Cp class=\"p\"\u003E Datasets extracted in a blind mode (e.g. without any previous knowledge of the source location and morphology) can be constructed rapidly, potentially reaching substantial sizes (up to millions of images) when using future full-sky surveys. Without additional selection processes, these datasets tend to be largely unbalanced, predominantly comprising frames composed entirely of compact sources. The \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E dataset also comprises frames with large-scale diffuse emission, including background or portions of very extended sources located along the Galactic plane. For simplicity, we have labelled them as \u003Cspan class=\"monospace\"\u003Ehulk\u003C\u002Fspan\u003E. In contrast, “smarter” datasets centered on selected source positions typically have smaller sizes, requiring significant efforts (catalogue production and source type annotation) for construction. We have labelled them as \u003Cspan class=\"monospace\"\u003Ebanner\u003C\u002Fspan\u003E. Indeed, one goal of this work is evaluating differences and benefits of both kind of datasets over different analysis tasks. Summary information for all produced datasets is reported in \u003Ca class=\"xref table\" href=\"#tbl1\"\u003ETable 1\u003C\u002Fa\u003E. In \u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E we display sample images from the \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (top panels), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (middle panels) and \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E (bottom panels) datasets.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" data-magellan-destination=\"tbl1\" id=\"tbl1\"\u003E\n\n\u003Cdiv class=\"caption\"\u003E\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003ETable 1.\u003C\u002Fspan\u003E Summary information of datasets used for SimCLR model training. The number of images \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline47.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"25\" height=\"12\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline47.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$n_{img}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E is reported in column (2). The image size \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline48.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"22\" height=\"12\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline48.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$s_{img}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E is reported in column (3). \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline49.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"22\" height=\"12\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline49.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$s_{img}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E is fixed for all images in the \u003Cspan class=\"monospace\"\u003Ehulk_smgp\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E datasets, while \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline50.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"22\" height=\"12\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline50.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$s_{img}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E is not fixed and depends on the source size \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline51.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"35\" height=\"9\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline51.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$s_{\\text{source}}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E (equivalent to the maximum source bounding box dimension) in the \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E datasets. For these datasets, we report the average, minimum and maximum source sizes in columns (4), (5) and (6), respectively. Images from all datasets are eventually resized to a fixed size for model training and testing (see \u003Ca class=\"xref sec\" href=\"#s2-3\"\u003ESection 2.3\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cspan\u003E\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab1.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"399\" height=\"155\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab1.png\" data-zoomable=\"false\"\u003E\u003C\u002Fdiv\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f2\" id=\"f2\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig2.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"5187\" height=\"5154\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig2.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 2.\u003C\u002Fspan\u003E Representative examples of images from the \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (top panels), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (middle panels) and \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (bottom panels) datasets. A zscale transform was applied to all images for visualization scopes. Top panels: sample images containing only compact sources (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E(a)), or multiple extended sources (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigures 2\u003C\u002Fa\u003E(b) and \u003Ca class=\"xref fig\" href=\"#f2\"\u003E2\u003C\u002Fa\u003E(c)). Middle panels: sample source with diffuse morphology (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E(d)), a multi-component extended source exhibiting typical radio galaxy morphology (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E(e)), a single-component extended source with a roundish morphology (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E(f)). Bottom panels: sample sources with FR-I (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E(g)), FR-II (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E(h)) and peculiar (\u003Ca class=\"xref fig\" href=\"#f2\"\u003EFigure 2\u003C\u002Fa\u003E(i)) classification.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s2-3\" id=\"s2-3\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E2.3\u003C\u002Fspan\u003E Data pre-processing and augmentation\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E For the training and inference stages, we applied these pre-processing steps to input images:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Grayscale images were converted to 3-channels. Each channel was processed differently from others, applying the following transformations:\u003Col class=\"list number nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E-\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EChannel 1\u003C\u002Fem\u003E: sigma-clipping (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline66.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"24\" height=\"10\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline66.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sigma_{low}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E = 5, \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline67.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"19\" height=\"13\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline67.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sigma_{up}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E = 30);\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E-\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EChannel 2\u003C\u002Fem\u003E: zscale transform (contrast = 0.25);\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E-\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EChannel 3\u003C\u002Fem\u003E: zscale transform (contrast = 0.4).\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Fol\u003E\n\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Each channel was independently normalized to a [0,1] range using a \u003Cem class=\"italic\"\u003EMinMax\u003C\u002Fem\u003E transformation;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Finally, each channel was resized to a 224\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline68.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline68.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E224 size in pixels.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E A key aspect when training contrastive learning models is the choice of applied data augmentation steps to make the model invariant with respect to non-physical properties or to features not related to the radio sources. We applied the following augmenters to the data sequentially:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003ERandomCropResize\u003C\u002Fem\u003E: randomly crop input images to size \u003Cspan class=\"monospace\"\u003Ecrop_size\u003C\u002Fspan\u003E \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline69.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline69.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E image size, and resize data to the original size. \u003Cspan class=\"monospace\"\u003Ecrop_size\u003C\u002Fspan\u003E was randomly varied in the range [0.8, 1.0];\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EColorJitter\u003C\u002Fem\u003E: apply a colour jitter transformation using all three image channels;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EFlip\u003C\u002Fem\u003E: random flip images either vertically or horizontally;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003ERotate\u003C\u002Fem\u003E: rotate images by either 90, 180 or 270 degrees;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EBlur\u003C\u002Fem\u003E: apply Gaussian blurring to images using a \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline70.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline70.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sigma$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E parameter randomly varied in the range [1,3];\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003ERandomThresholding\u003C\u002Fem\u003E: threshold each channel separately using a per-channel percentile threshold randomly varied in the range [40,60].\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E The \u003Cem class=\"italic\"\u003ERandomThresholding\u003C\u002Fem\u003E augmenter was introduced to make the model less dependent on image background features. This stage was not applied when training over the \u003Cspan class=\"monospace\"\u003Ebanner\u003C\u002Fspan\u003E datasets, as images in this dataset are already zoomed on radio sources, and thus the background would likely not be estimated correctly. Furthermore, not all augmenters are applied to every image in the training dataset. In \u003Ca class=\"xref table\" href=\"#tbl2\"\u003ETable 2\u003C\u002Fa\u003E we provide a summary of augmenter steps used in the pre-processing pipeline with their parameters, including the probability with which each data transform is applied to images. With respect to Chen et al. (2020), we reduced the fraction of random cropping allowed to avoid cutting out relevant details of extended sources from the resulting image.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s2-4\" id=\"s2-4\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E2.4\u003C\u002Fspan\u003E Model training\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E We trained a SimCLR model on each of the four datasets described in \u003Ca class=\"xref sec\" href=\"#s2-2\"\u003ESection 2.2\u003C\u002Fa\u003E, using the hyperparameters listed in \u003Ca class=\"xref table\" href=\"#tbl3\"\u003ETable 3\u003C\u002Fa\u003E. We will refer to them using their training dataset name: \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E, and \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E. A fourth model, referred to as \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E hereafter, was trained in two steps, first on the \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E dataset and then on the \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E dataset. The final model weights from the first step were used as initialization for the second step. For all models, we used a \u003Cem class=\"italic\"\u003EResNet18\u003C\u002Fem\u003E (He et al., \u003Ca class=\"xref bibr\" href=\"#ref20\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference He\u003C\u002Fspan\u003E2016\u003C\u002Fa\u003E) encoder and a 2-layer projector with 256 and 128 neurons, respectively.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" data-magellan-destination=\"tbl2\" id=\"tbl2\"\u003E\n\n\u003Cdiv class=\"caption\"\u003E\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003ETable 2.\u003C\u002Fspan\u003E List of augmentations used in SimCLR model training. In column (2) we reported the transform parameter values. In column (3) we reported the probability used to apply the transform in the augmentation pipeline, e.g. 1.0 means the transform is always applied to all input images.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cspan\u003E\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab2.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"382\" height=\"265\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab2.png\" data-zoomable=\"false\"\u003E\u003C\u002Fdiv\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" data-magellan-destination=\"tbl3\" id=\"tbl3\"\u003E\n\n\u003Cdiv class=\"caption\"\u003E\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003ETable 3.\u003C\u002Fspan\u003E List of hyperparameters used in SimCLR model training.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cspan\u003E\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab3.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"382\" height=\"265\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab3.png\" data-zoomable=\"false\"\u003E\u003C\u002Fdiv\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003Cp class=\"p\"\u003E Following Chen et al. (2020), all training runs began with a linear warm-up phase lasting 10 epochs, after which we switched to a cosine learning rate decay strategy. In total, we trained models for 500 epochs on the \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E datasets. A smaller total number of epochs (100) was used when training over the larger \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E datasets to reduce computational costs.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Training runs were performed on three different computing server nodes, each equipped with a GPU device:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Node A: 48 cores (Intel Xeon Gold 6248R CPU, 3.00 GHz), 512 GB RAM, NVIDIA Quadro RTX 6000 (24 GB)\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Node B: 24 cores (Intel Xeon Silver 4410Y, 2.00 GHz), 256 GB RAM, NVIDIA A30 (24 GB)\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Node C: 36 cores (Intel Xeon CPU E5-2697 v4, 2.30 GHz), 128 GB RAM, NVIDIA Tesla V100 (16 GB)\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E Typical training times over the \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E dataset are of the order of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline73.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline73.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E6.7 hours\u002Fepoch on nodes A\u002FB, and \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline74.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline74.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E12.5 hours\u002Fepoch on node C.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s2-5\" id=\"s2-5\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E2.5\u003C\u002Fspan\u003E Evaluation of downstream tasks\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E In the following sections, the trained self-supervised models and corresponding data representation will be evaluated on radio source classification (\u003Ca class=\"xref sec\" href=\"#s3\"\u003ESection 3\u003C\u002Fa\u003E) and detection (\u003Ca class=\"xref sec\" href=\"#s4\"\u003ESection 4\u003C\u002Fa\u003E) tasks using supervised CNN classifiers trained on labelled datasets. Furthermore, in \u003Ca class=\"xref sec\" href=\"#s5\"\u003ESection 5\u003C\u002Fa\u003E we will use the self-supervised features to classify radio images according to the morphology of hosted sources in a supervised way and according to their peculiarity degree in a completely unsupervised way. To estimate the performances achieved in these downstream tasks, we will consistently use these widely adopted metrics in multi-class problems:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003ERecall\u003C\u002Fem\u003E (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline75.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"13\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline75.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathcal{R}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E): Fraction of sources (images) of a given class that were correctly classified by the model out of all sources (images) labelled in that class, computed as: \u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\" data-magellan-destination=\"udisp1\" id=\"udisp1\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU1.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"91\" height=\"34\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU1.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n\\begin{equation*}\\mathcal{R}=\\frac{TP}{TP + FN}\\end{equation*}\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EPrecision\u003C\u002Fem\u003E (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline76.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline76.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathcal{P}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E): Fraction of sources (images) correctly classified as belonging to a specific class, out of all sources (images) the model predicted to belong to that class, computed as:\u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\" data-magellan-destination=\"udisp2\" id=\"udisp2\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU2.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"87\" height=\"34\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU2.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n\\begin{equation*}\\mathcal{P}=\\frac{TP}{TP + FP}\\end{equation*}\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EContamination\u003C\u002Fem\u003E (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline77.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline77.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\mathcal{C}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E): Fraction of sources (images) of a given class incorrectly classified as belonging to a specific class, out of all sources (images) the model predicted to belong to that class, computed as: \u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\" data-magellan-destination=\"udisp3\" id=\"udisp3\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU3.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"142\" height=\"33\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqnU3.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n\\begin{equation*}\\mathcal{C}= \\frac{FP}{TP + FP}= 1 - \\mathcal{P}\\end{equation*}\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EF1-score\u003C\u002Fem\u003E: the harmonic mean of precision and recall: \u003C\u002Fp\u003E\u003Cdiv data-mathjax-status=\"alt-graphic\" class=\"disp-formula\" data-magellan-destination=\"disp4\" id=\"disp4\"\u003E\n\u003Cspan class=\"disp-formula-label\"\u003E(4)\u003C\u002Fspan\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn4.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"145\" height=\"34\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_eqn4.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n\\begin{equation}\\text{F1-score}=2\\times\\frac{\\mathcal{P}\\times\\mathcal{R}}{\\mathcal{P}+\\mathcal{R}}\\end{equation}\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E where \u003Cem class=\"italic\"\u003ETP\u003C\u002Fem\u003E, \u003Cem class=\"italic\"\u003EFN\u003C\u002Fem\u003E, \u003Cem class=\"italic\"\u003EFP\u003C\u002Fem\u003E are the number of true positive, false negative and false positive instances, respectively.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec other\" data-magellan-destination=\"s3\" id=\"s3\"\u003E\n\n\u003Ch2 class=\"A\"\u003E\u003Cspan class=\"label\"\u003E3.\u003C\u002Fspan\u003E Task I: Classification of radio source morphology\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E In this section, we quantitatively evaluate the learned self-supervised representation on a source morphology classification problem.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Morphological classification plays a pivotal role in radio astronomy, enabling scientists to gain insights into the underlying source nature from the observed shape and structures. The majority of existing works in the radio image domain are targeted for extragalactic science objectives, focusing on classification of radio galaxies (see for example Aniyan & Thorat \u003Ca class=\"xref bibr\" href=\"#ref1\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Aniyan and Thorat\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E, Ma et al., \u003Ca class=\"xref bibr\" href=\"#ref34\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Ma\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E, or Ndung’u et al., \u003Ca class=\"xref bibr\" href=\"#ref39\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Ndung’u\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E for a recent review) in different morphological classes: \u003Cspan class=\"monospace\"\u003Ecompact\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EFR-I\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EFR-II\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003Ebent-tailed\u003C\u002Fspan\u003E (including WAT\u003Ca class=\"xref fn\" href=\"#fn5\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ee\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E and NAT\u003Ca class=\"xref fn\" href=\"#fn6\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ef\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E population), \u003Cspan class=\"monospace\"\u003Eirregular\u003C\u002Fspan\u003E (including, for example, X-shaped or ring-like radio galaxies).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f3\" id=\"f3\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig3.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"5187\" height=\"3526\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig3.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 3.\u003C\u002Fspan\u003E Sample images from the RGZ dataset with representative sources of different morphological classes (reported below each frame). A zscale transform was applied to all images for visualization scopes.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E Morphological classification is also an important post-detection stage to filter extracted sources by general morphology (e.g. compact vs extended sources) for specialized source property measurements or other advanced classification analysis. In this context, the adopted source labelling scheme is rather general-purpose and domain-agnostic, suited to be eventually refined afterwards. For example, typical used labels are \u003Cspan class=\"monospace\"\u003EPOINT-LIKE\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003ERESOLVED\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E or labels that contain information about the number of radio components present in the extracted source (as in Wu et al., \u003Ca class=\"xref bibr\" href=\"#ref58\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Wu\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The analysis carried out in this section falls into the second use-case scenario. This choice is mostly driven by existing datasets. Available annotated datasets for radio galaxy classification (mostly based on VLA FIRST survey data) are, in fact, rather limited in size (e.g. typically <100-200 images per class, <2000 images overall) and would currently prevent us from obtaining a robust evaluation of our self-supervised models over multiple test set realizations. For example, the \u003Cem class=\"italic\"\u003EMirabest\u003C\u002Fem\u003E dataset (Porter & Scaife \u003Ca class=\"xref bibr\" href=\"#ref44\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Porter and Scaife\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) contains 1256 source images of balanced FR-I\u002FFR-II radio galaxy classes, out of which 833 images constitute the “Confident” sample, and the rest (423 images) the “Uncertain” sample. On this dataset, Slijepcevic et al. (\u003Ca class=\"xref bibr\" href=\"#ref50\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Slijepcevic\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E) reported an improvement of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline78.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline78.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E3-4% in classification performance of a self-supervised pre-trained model with respect to a fully supervised model trained from scratch on the “Confident” sample (or on a portion of it). Classification metrics were, however, estimated on the “Uncertain” sample, and hence the observed enhancement is due to less than 20 sources. We, therefore, opted for this work to use a larger dataset (roughly by one order of magnitude) and perform a similar analysis once a larger dataset is assembled within the ASKAP EMU survey.\u003C\u002Fp\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s3-1\" id=\"s3-1\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E3.1\u003C\u002Fspan\u003E Dataset\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E For this analysis, we considered data from the Radio Galaxy Zoo (RGZ) project\u003Ca class=\"xref fn\" href=\"#fn7\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Eg\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E (Banfield et al., \u003Ca class=\"xref bibr\" href=\"#ref2\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Banfield\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E). This includes radio images of size 3’\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline79.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline79.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E 3’ from the VLA Faint Images of the Radio Sky at Twenty cm (FIRST) survey (1.4 GHz, angular resolution \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline80.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline80.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E5\u003Csup class=\"sup\"\u003E′′\u003C\u002Fsup\u003E) (Becker et al., \u003Ca class=\"xref bibr\" href=\"#ref3\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Becker\u003C\u002Fspan\u003E1995\u003C\u002Fa\u003E). Radio sources found in these images were labelled into multiple morphological classes, on the basis of the observed number of components (C) and peaks (P) (see Wu et al. \u003Ca class=\"xref bibr\" href=\"#ref58\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Wu\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E for more details on the classification schema). Angular size is also available for each source.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In this analysis, we extracted 82 084 image cutouts around radio sources that have been classified in the RGZ Data Release 1 (DR1) with a consensus level \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline81.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"11\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline81.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\ge$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E0.6 in the following classes: 1C-1P (55.0%), 1C-2P (20.9%), 1C-3P (1.9%), 2C-2P (17.6%), 2C-3P (2.0%), 3C-3P (2.5%). We assumed a cutout size equal to 1.5 \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline82.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline82.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E the source angular size, as listed in the RGZ catalogue. A representative image of each source morphological category is shown in \u003Ca class=\"xref fig\" href=\"#f3\"\u003EFigure 3\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E As the full dataset is largely unbalanced towards sources of class morphology 1C-1P, we randomly created \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline83.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"26\" height=\"12\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline83.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$N_{sets}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E = 5 balanced training and test sets having 1000 and 600 images per class, respectively. Both training and test set images were pre-processed as described in \u003Ca class=\"xref sec\" href=\"#s2-3\"\u003ESection 2.3\u003C\u002Fa\u003E for the SimCLR model training.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s3-2\" id=\"s3-2\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E3.2\u003C\u002Fspan\u003E Evaluation of self-supervised representation\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E In \u003Ca class=\"xref fig\" href=\"#f4\"\u003EFigure 4\u003C\u002Fa\u003E we present a two-dimensional projection, obtained with the \u003Cem class=\"italic\"\u003EUniform Manifold Approximation and Projection\u003C\u002Fem\u003E (UMAP) (McInnes et al., \u003Ca class=\"xref bibr\" href=\"#ref35\"\u003E2018\u003C\u002Fa\u003E) dimensionality reduction algorithm, of the representation vector (original size equal to 512) produced by the trained \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E model on the RGZ dataset. As can be observed, the self-supervised model effectively groups sources of different morphological class in distinct areas of the latent space. No isolated clusters are discernible in the projected two-dimensional UMAP feature space, as well as in a PCA scatter plot of top-2 features (not shown here). Nevertheless, these or similar diagnostic plots, can be useful for potentially identifying possible image mislabeling in the dataset, e.g. sources that fall within a region that is predominantly populated by other classes.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f4\" id=\"f4\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig4.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2081\" height=\"1966\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig4.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 4.\u003C\u002Fspan\u003E 2D UMAP projection of the data representation vector (size = 512) produced by the trained \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E model on the RGZ dataset.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E We carried out a classification analysis using a CNN classifier with a standard architecture: a \u003Cem class=\"italic\"\u003EResNet18\u003C\u002Fem\u003E backbone model (as in the SimCLR model) followed by a classification head. The latter consists of a single layer followed by a softmax activation, representing the predicted probability distribution over the set of classes. To evaluate the quality of the self-supervised representation, we froze the backbone model, setting and fixing its weights to those obtained in the trained SimCLR models, and trained only the classification head on RGZ training datasets for a limited number of epochs (30). We considered only rotation and flipping transformations as augmentation steps during the training.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In \u003Ca class=\"xref fig\" href=\"#f5\"\u003EFigure 5\u003C\u002Fa\u003E we report the classification F1-scores obtained on the test set by different self-supervised pre-trained models: \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (red squares), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (blue inverted triangles), \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E (green triangles), \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (orange diamonds), \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E (cyan asterisks). The reported values and their errors are respectively the F1-score mean and mean error computed over the available test sets. These metrics were compared against those obtained with a baseline model pre-trained on the \u003Cspan class=\"monospace\"\u003EImageNet-1k\u003C\u002Fspan\u003E dataset\u003Ca class=\"xref fn\" href=\"#fn8\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Eh\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E Deng et al., \u003Ca class=\"xref bibr\" href=\"#ref11\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Deng\u003C\u002Fspan\u003E2009\u003C\u002Fa\u003E) (trained on non-radio data), shown with black dots in \u003Ca class=\"xref fig\" href=\"#f5\"\u003EFigure 5\u003C\u002Fa\u003E. We found that self-supervised pre-trained models reach approximately 7–12% better overall scores with respect to the baseline, due to the higher quality features obtained on complex and extended sources, which are not as well represented in the \u003Cem class=\"italic\"\u003EImageNet\u003C\u002Fem\u003E dataset. Another valuable indication is that the two-step pre-training approach done for the \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E model training provide better results compared to training over random or source-centred images alone. The improvement is, however, not very significant with respect to the \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E, likely due to both the limited size of the \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E dataset and the absence of Galactic-like diffuse and extended sources in the RGZ dataset. By construction, we expect that the \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E model should be more specialized for this kind of source morphologies. This will be tested in a future analysis once we finalize a new test dataset with diffuse sources taken from ASKAP EMU observations.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f5\" id=\"f5\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig5.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2163\" height=\"1865\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig5.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 5.\u003C\u002Fspan\u003E Classification F1-scores obtained for different classes and for all classes cumulatively over RGZ test sets with different pre-trained and frozen backbone models: \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (red squares), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (blue inverted triangles), \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E (green triangles), \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (orange diamonds), \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E (cyan asterisks), \u003Cspan class=\"monospace\"\u003EImageNet\u003C\u002Fspan\u003E (black dots). The reported values and errors are the F1-score mean and mean error computed over five test sets.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E In \u003Ca class=\"xref fig\" href=\"#f6\"\u003EFigure 6\u003C\u002Fa\u003E we report the confusion matrix obtained over the RGZ test sample with a \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E pre-trained and frozen backbone model. The obtained misclassification rates suggest that a considerable fraction (10% to 20%) of sources, particularly those with two or three components, may be hard to be correctly distinguished from other classes. After a visual inspection of the misclassified sources, we found that in some cases the misclassification is rather due to dataset mislabelling, e.g. the ground truth label present in the dataset is not correct and the model is indeed predicting the expected class. Some examples are reported in \u003Ca class=\"xref fig\" href=\"#f13\"\u003EFigure A.1\u003C\u002Fa\u003E. Future analysis should therefore take into consideration a revision of the RGZ dataset annotation.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f6\" id=\"f6\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig6.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2427\" height=\"1911\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig6.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 6.\u003C\u002Fspan\u003E Confusion matrix of the source morphology classifier (trained with \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E pre-trained and frozen backbone model) obtained over the RGZ test set.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s3-3\" id=\"s3-3\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E3.3\u003C\u002Fspan\u003E Model fine-tuning\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E We fine-tuned the source classifier by unfreezing backbone model layers (e.g. training them along with the classification head) and compared the accuracies reached by two models: one initialized with random weights (e.g. training from \u003Cem class=\"italic\"\u003Escratch\u003C\u002Fem\u003E), and the other with backbone model weights initialized to the \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E backbone model weights (best performing model found in \u003Ca class=\"xref sec\" href=\"#s3-2\"\u003ESection 3.2\u003C\u002Fa\u003E). We compared the results of both models when trained on the full training sets and when trained on smaller training sets, obtained by gradually removing labelled data randomly from the original set. In all cases, models were trained for 150 epochs. The test sets were kept unchanged to compute the classification accuracies. This was done to study how the model performs in the recurring scenario in which the amount of labelled data is significantly limited. We reported the results in \u003Ca class=\"xref fig\" href=\"#f7\"\u003EFigure 7\u003C\u002Fa\u003E. As can be seen, the fully supervised model (trained from scratch) becomes almost untrainable, providing poor classification metrics, in the small number of labels regime. This occurs for the RGZ dataset below a fraction of approximately 10% of the original training dataset, corresponding to about 600 images (e.g. \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline84.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline84.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E100 images per class). On the other hand, self-supervised pre-training enables to fine-tune the model even with few labels, achieving considerably better metrics (>20%). Above the 10% label fraction threshold, the fully supervised model achieved slightly better scores, highlighting that no significant performance benefits are obtained from the pre-training process, at least with the model and dataset sample sizes available for this work. This result is qualitatively on par with the results of the transfer learning analysis carried out by Chen et al. (2020) (Section B.8.2) on 12 natural image datasets (Food, CIFAR10, CIFAR100,) with \u003Cem class=\"italic\"\u003EResNet50\u003C\u002Fem\u003E architectures of different widths (x1, x2, x4). The authors compared the fine-tuning classification accuracies reached by SimCLR against a supervised model baseline. With wider networks (\u003Cem class=\"italic\"\u003EResNet50\u003C\u002Fem\u003E x4), the self-supervised model was found to outperform the supervised one in 7 datasets (Chen et al. 2020, Table 8). The opposite was however observed with the narrower \u003Cem class=\"italic\"\u003EResNet50\u003C\u002Fem\u003E, where the supervised baseline best performed in 10 datasets (Chen et al. 2020, Table B5) out of 12. Our analysis, carried out with an even smaller network (\u003Cem class=\"italic\"\u003EResNet18\u003C\u002Fem\u003E), may well fall into the latter case. In either cases, the observed accuracy differences are smaller than 1% for most datasets.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f7\" id=\"f7\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig7.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2156\" height=\"2170\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig7.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 7.\u003C\u002Fspan\u003E Classification F1-scores obtained (for all classes cumulatively) over RGZ test sets as a function of the number of images \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline85.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"30\" height=\"10\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline85.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$n_{train}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E in the training set with two alternative models: one trained from scratch (open black dots), the other trained with backbone model weights initialized to \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E weights (filled black dots). The upper x-axis indicates the fraction of the full training set considered in each training run.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec other\" data-magellan-destination=\"s4\" id=\"s4\"\u003E\n\n\u003Ch2 class=\"A\"\u003E\u003Cspan class=\"label\"\u003E4.\u003C\u002Fspan\u003E Task II: Radio source detection\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E In this section, we quantitatively evaluate the learned self-supervised representation on an instance segmentation problem, specifically the detection of radio sources with various morphologies.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Algorithms used in traditional radio source finders are not well-suited for detecting extended radio sources with diffuse edges, and they are unable to detect extended sources that are composed of multiple disjoint regions. To address this limitation, new source finders (Wu et al., \u003Ca class=\"xref bibr\" href=\"#ref58\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Wu\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E; Mostert et al., \u003Ca class=\"xref bibr\" href=\"#ref38\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Mostert\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E; Zhang et al., \u003Ca class=\"xref bibr\" href=\"#ref59\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Zhang\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E; Yu et al., \u003Ca class=\"xref bibr\" href=\"#ref56\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Yu\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E; Riggi et al., \u003Ca class=\"xref bibr\" href=\"#ref47\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E; Lao et al., \u003Ca class=\"xref bibr\" href=\"#ref28\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lao\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E; Gupta et al., \u003Ca class=\"xref bibr\" href=\"#ref17\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E; Cornu et al., \u003Ca class=\"xref bibr\" href=\"#ref10\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Cornu\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E) based on deep neural networks and object detection frameworks have been developed and trained on either simulated or real radio data. Core components of these models are deep CNN backbones and transformer architectures, both of which have millions of parameters that need to be optimized during training. Although these models offer a substantial advancement in extended radio galaxy detection, their performance is limited by the small size (few thousand images) and the imbalance of objects in the available radio training datasets. Additionally, there is a potential performance drop (up to 10% in Riggi et al., \u003Ca class=\"xref bibr\" href=\"#ref47\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) when transferring a trained model to data produced by a different survey or telescope, especially if the new data has a better angular resolution (Tang et al., \u003Ca class=\"xref bibr\" href=\"#ref52\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Tang\u003C\u002Fspan\u003E2019\u003C\u002Fa\u003E). To improve the training stage, it is a common practice to use models pre-trained on much larger annotated samples of non-astronomical images, such as the \u003Cem class=\"italic\"\u003EImageNet-1k\u003C\u002Fem\u003E (Deng et al., \u003Ca class=\"xref bibr\" href=\"#ref11\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Deng\u003C\u002Fspan\u003E2009\u003C\u002Fa\u003E, \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline86.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline86.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E1.28 million images) or the \u003Cem class=\"italic\"\u003ECOCO\u003C\u002Fem\u003E (Tsung-Yi et al. \u003Ca class=\"xref bibr\" href=\"#ref53\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Tsung-Yi\u003C\u002Fspan\u003E2014\u003C\u002Fa\u003E, 328 000 images) datasets. In this scenario, it is worth exploring whether foundational models built with self-supervised methods on unlabelled radio data can offer performance benefits over non-radio foundational models, especially with small datasets.\u003C\u002Fp\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s4-1\" id=\"s4-1\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E4.1\u003C\u002Fspan\u003E caesar-mrcnn source detector\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E For this analysis, we used the \u003Cem class=\"italic\"\u003Ecaesar-mrcnn\u003C\u002Fem\u003E source detector (Riggi et al., \u003Ca class=\"xref bibr\" href=\"#ref47\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E), based on the Mask R-CNN object detection framework (He et al., \u003Ca class=\"xref bibr\" href=\"#ref23\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference He\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E), to extract source segmentation masks and predicted class labels from input radio images. With respect to our original work (Riggi et al., \u003Ca class=\"xref bibr\" href=\"#ref47\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E), we have upgraded the software to TensorFlow 2.x, producing a new refactored version\u003Ca class=\"xref fn\" href=\"#fn9\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ei\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E with an improved data pre-processing pipeline and support for additional backbone models.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In this context, we would like to make a brief preamble and clarify the motivations that guided the development of the \u003Cem class=\"italic\"\u003Ecaesar-mrcnn\u003C\u002Fem\u003E source detector, as these were either misinterpreted or inaccurately presented in other works. Additionally, we aim to address certain conceptual aspects that we realize are often source of confusion within this field.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E It is essential to recognize that source detection (or extraction), classification and source characterization (or measurement) represent distinct conceptual stages. A source detector, to be defined as such, should focus solely on extracting source bounding boxes or, preferably, pixel masks, which are the inputs required for the source measurement or classification stages. The source measurement step, on the other hand, is responsible for estimating source properties such as position, flux density, and shape from the outputs of the source detection. Strictly speaking, this step is not required in a source detector, as assumed in Lao et al. (\u003Ca class=\"xref bibr\" href=\"#ref28\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lao\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E). From a methodological standpoint, it is advisable to avoid conflating these stages. This may allow addressing numerous use cases simultaneously, but it can also be counterproductive, leading, for example, to design compromises and overly complex models with multiple loss components to be balanced during training. The resulting models likely have a higher chance of underperforming on both tasks (detection or characterization) with respect to models that are designed and optimised for a specific task. For this reason, source characterization metrics should be independently evaluated and not mixed with the detection metrics, as required, for example, in the SKA Data Challenge 1 (Bonaldi et al., \u003Ca class=\"xref bibr\" href=\"#ref5\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Bonaldi\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) scoring function. When we designed the \u003Cem class=\"italic\"\u003Ecaesar-mrcnn\u003C\u002Fem\u003E source detector, we deliberately did not provide a source characterization stage. As we already implemented source measurement functions in the \u003Cem class=\"italic\"\u003Ecaesar\u003C\u002Fem\u003E source finder, we rather aim to interface both codes and, at best, add new developments for improvements in specific areas, such as low S\u002FN source characterization and source deblending, as discussed in Boyce et al. (\u003Ca class=\"xref bibr\" href=\"#ref8\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Boyce\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In recent ML-based source extractors, source classification was typically performed alongside the detection step, often to classify extracted sources into compact and extended classes of radio galaxies (FR-I, FR-II, etc.). We aimed for our source detector to be general-purpose, portable, and not tied to a specific radioastronomical domain. Therefore, in our view, the detection step should, at a minimum, classify between real and spurious sources, or, at most, between domain-agnostic morphological classes. More refined or domain-specific classification schemes can be more effectively applied afterwards in specialized classifiers working on source-centered images obtained from the detection step. These considerations were the rationale behind the general class labeling scheme adopted in \u003Cem class=\"italic\"\u003Ecaesar-mrcnn\u003C\u002Fem\u003E (briefly reported in the following Section).\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s4-2\" id=\"s4-2\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E4.2\u003C\u002Fspan\u003E Dataset\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E To train and test \u003Cem class=\"italic\"\u003Ecaesar-mrcnn\u003C\u002Fem\u003E, we considered the dataset described in Riggi et al., \u003Ca class=\"xref bibr\" href=\"#ref47\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E), which contains 12 774 annotated radio images from different surveys, including VLA FIRST, ATCA Scorpio (Umana et al., \u003Ca class=\"xref bibr\" href=\"#ref54\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Umana\u003C\u002Fspan\u003E2015\u003C\u002Fa\u003E), and ASKAP-EMU Scorpio (Umana et al., \u003Ca class=\"xref bibr\" href=\"#ref55\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Umana\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E). The annotation data consist of pixel segmentation masks and classification labels for a total of 38 342 objects (both real and spurious sources) present in the dataset images. Five object classes were defined:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003ESPURIOUS\u003C\u002Fspan\u003E: imaging artefacts around bright sources, having a ring-like or elongated compact morphology;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E: single-island isolated point- or slightly resolved compact radio sources with one or more blended components, each with morphology similar to the synthesized beam shape;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E: radio sources with a single-island extended morphology, with one or more blended components, some morphologically different from the synthesized beam shape;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EEXTENDED-MULTISLAND\u003C\u002Fspan\u003E: radio sources with an extended morphology, consisting of more than one island, each eventually containing one or more blended components, having a point-like or an extended morphology;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EFLAGGED\u003C\u002Fspan\u003E: poorly-imaged single-island radio sources, highly contaminated by nearby imaging artefacts.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E For more details on the dataset labelling schema and rationale, we refer the reader to the original work. We also define a generic class label \u003Cspan class=\"monospace\"\u003ESOURCE\u003C\u002Fspan\u003E for analysis purposes, including real and non-flagged sources, i.e. object instances of class \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E, or \u003Cspan class=\"monospace\"\u003EEXTENDED-MULTISLAND\u003C\u002Fspan\u003E. Though it is planned, the dataset does not presently contain images and annotation data for Galactic diffuse objects. Indeed, none of existing ML-based finders have been trained to detect diffuse sources other than radio galaxy diffuse structures (e.g. lobe components). The latter are the only diffuse structures present in our dataset, but we never noted to obtain poor detection performances on them, as reported in Ndung’u et al. (\u003Ca class=\"xref bibr\" href=\"#ref39\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Ndung’u\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In \u003Ca class=\"xref fig\" href=\"#f8\"\u003EFigure 8\u003C\u002Fa\u003E we present sample images from the dataset, including representative sources for each class. Given that the current dataset is significantly skewed towards compact sources (comprising approximately 80% of the annotated objects), we created five re-balanced training samples, each containing 3245 images, with the following class distributions: \u003Cspan class=\"monospace\"\u003ESPURIOUS\u003C\u002Fspan\u003E (1464 objects, 14.4%), \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E (5457 objects, 53.6%), \u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E (2042 objects, 20.1%), \u003Cspan class=\"monospace\"\u003EEXTENDED-MULTISLAND\u003C\u002Fspan\u003E (1047, 10.3%), \u003Cspan class=\"monospace\"\u003EFLAGGED\u003C\u002Fspan\u003E (169 objects, 1.7%). The remaining data was reserved to create five test samples, each containing 5110 images, with the following class distributions: \u003Cspan class=\"monospace\"\u003ESPURIOUS\u003C\u002Fspan\u003E (1022 objects, 6.6%), \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E (12.346 objects, 80.0%), \u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E (1307 objects, 8.5%), \u003Cspan class=\"monospace\"\u003EEXTENDED-MULTISLAND\u003C\u002Fspan\u003E (636, 4.1%), \u003Cspan class=\"monospace\"\u003EFLAGGED\u003C\u002Fspan\u003E (122 objects, 0.8%).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f8\" id=\"f8\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig8.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"5186\" height=\"1392\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig8.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 8.\u003C\u002Fspan\u003E Sample images (taken from Riggi \u003Ca class=\"xref bibr\" href=\"#ref47\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) from the dataset used for \u003Cem class=\"italic\"\u003Ecaesar-mrcnn\u003C\u002Fem\u003E training\u002Ftesting, including objects of different classes: a \u003Cspan class=\"monospace\"\u003EFLAGGED\u003C\u002Fspan\u003E object (\u003Ca class=\"xref fig\" href=\"#f8\"\u003EFigure 8\u003C\u002Fa\u003E(a), in gray), \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E objects (in blue), a \u003Cspan class=\"monospace\"\u003EMULTI-ISLAND\u003C\u002Fspan\u003E object (\u003Ca class=\"xref fig\" href=\"#f8\"\u003EFigure 8\u003C\u002Fa\u003E(b), in orange), \u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E objects (\u003Ca class=\"xref fig\" href=\"#f8\"\u003EFigure 8\u003C\u002Fa\u003E(c), in yellow), \u003Cspan class=\"monospace\"\u003ESPURIOUS\u003C\u002Fspan\u003E objects (\u003Ca class=\"xref fig\" href=\"#f8\"\u003EFigure 8\u003C\u002Fa\u003E(d), in red).\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s4-3\" id=\"s4-3\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E4.3\u003C\u002Fspan\u003E Evaluation of self-supervised representation\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E To assess the effectiveness of the self-supervised representation, we followed the procedure outlined in \u003Ca class=\"xref sec\" href=\"#s3-2\"\u003ESection 3.2\u003C\u002Fa\u003E. We froze the Mask R-CNN \u003Cem class=\"italic\"\u003EResNet18\u003C\u002Fem\u003E backbone model, setting and keeping its weights fixed to those obtained in the trained SimCLR models, and trained the remaining components (region proposal network, classification and bounding box regression head, mask prediction head) on multiple training datasets for a set number of epochs (250). The parameters of Mask R-CNN were configured to match the values optimized in our previous work (refer to Riggi \u003Ca class=\"xref bibr\" href=\"#ref47\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E, Table A1). We applied the same pre-processing transformations used for training the self-supervised models (as detailed in \u003Ca class=\"xref sec\" href=\"#s2-3\"\u003ESection 2.3\u003C\u002Fa\u003E). During training, we applied three distinct image augmentations: rotation, horizontal\u002Fvertical flipping, and zscale transformation with random contrast in the range of 0.25 to 0.4.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The performance of source detection was evaluated on the test sets using the metrics\u003Ca class=\"xref fn\" href=\"#fn10\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ej\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E defined in \u003Ca class=\"xref sec\" href=\"#s2-5\"\u003ESection 2.5\u003C\u002Fa\u003E and the following detection\u002Fclassification criteria:\u003C\u002Fp\u003E\u003Col class=\"list number nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E1.\u003C\u002Fspan\u003E Object detection score threshold equal to 0.5;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E2.\u003C\u002Fspan\u003E Intersection-over-Union (IoU) match threshold between detected and ground truth object masks equal to 0.6;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E3.\u003C\u002Fspan\u003E Object classified in the \u003Cspan class=\"monospace\"\u003ESOURCE\u003C\u002Fspan\u003E class group.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Fol\u003E\n\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f9\" id=\"f9\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig9.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2214\" height=\"2068\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig9.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 9.\u003C\u002Fspan\u003E Mask R-CNN object detection F1-score metric obtained for different object classes over multiple test sets with different pre-trained and frozen backbone models: \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (red squares), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (blue iverted triangles), \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E (green triangles), \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (orange diamonds), \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E (cyan asterisks), \u003Cspan class=\"monospace\"\u003EImageNet\u003C\u002Fspan\u003E (black dots). The reported values and errors are the means and mean errors computed over 5 test sets.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E The above metrics were computed for each class label and reported in \u003Ca class=\"xref fig\" href=\"#f9\"\u003EFigure 9\u003C\u002Fa\u003E for different models trained with frozen self-supervised backbone model weights: \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (red squares), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (blue triangles), \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E (green triangles), \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (orange diamonds). Metrics obtained with frozen \u003Cem class=\"italic\"\u003EImageNet\u003C\u002Fem\u003E weights are shown with black dots. The performance boost obtained with self-supervised models is significant, around 15%-20% for most classes, and even larger for multi-island sources and imaging artefacts. This is somehow expected, given that these structures are not present in the \u003Cem class=\"italic\"\u003EImageNet\u003C\u002Fem\u003E dataset. Overall, for the source class group we are interested in, we did not notice significant differences among trained self-supervised models, after taking into account the run-to-run statistical uncertainties on the obtained metrics. We will therefore consider a representative model (\u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E) in the following fine-tuning analysis.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s4-4\" id=\"s4-4\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E4.4\u003C\u002Fspan\u003E Model fine-tuning\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E We fine-tuned the Mask R-CNN model using random initialization weights (training from \u003Cem class=\"italic\"\u003Escratch\u003C\u002Fem\u003E) and weights initialized to \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E self-supervised model. We computed the object detection metrics over the source class group as a function of the training sample size, following the same approach discussed in \u003Ca class=\"xref sec\" href=\"#s3-3\"\u003ESection 3.3\u003C\u002Fa\u003E. Results are reported in \u003Ca class=\"xref fig\" href=\"#f10\"\u003EFigure 10\u003C\u002Fa\u003E. Black filled dots are the F1-scores obtained with the pre-trained \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E model, while open black dots are those found when training from scratch. In this case, we did not observe a significant benefit from using self-supervised pre-training compared to the source classification task studied in \u003Ca class=\"xref sec\" href=\"#s3\"\u003ESection 3\u003C\u002Fa\u003E. The improvement in performance in the low label regime (<10% of the original training sample size) is, in fact, of the order of a few percent. This behaviour highlights that other Mask R-CNN components likely play a major role in the overall model detection performance with respect to the backbone model.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f10\" id=\"f10\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig10.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2156\" height=\"2170\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig10.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 10.\u003C\u002Fspan\u003E Mask R-CNN object detection F1-score metric obtained over the \u003Cspan class=\"monospace\"\u003ESOURCE\u003C\u002Fspan\u003E class over multiple test sets as a function of the number of images \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline87.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"30\" height=\"10\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline87.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$n_{train}$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E in the training set with two alternative models: one trained from scratch (open markers), the other trained with backbone model weights initialized to \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E weights (filled markers). The upper x-axis indicates the fraction of the full training set considered in each training run.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec other\" data-magellan-destination=\"s5\" id=\"s5\"\u003E\n\n\u003Ch2 class=\"A\"\u003E\u003Cspan class=\"label\"\u003E5.\u003C\u002Fspan\u003E Task III: Search for peculiar objects\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E In this section, we quantitatively evaluated the learned self-supervised representations in an anomaly detection problem, i.e. employing them for an unsupervised search of radio objects with peculiar morphologies.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Next-generation radio surveys carried out with SKA precursor telescopes are already generating a huge amount of data. Serendipitous discoveries were already reported and obtained by visual inspection of the observed maps. For instance, Norris et al. (\u003Ca class=\"xref bibr\" href=\"#ref42\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Norris\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003Eb) and Koribalski et al. (\u003Ca class=\"xref bibr\" href=\"#ref26\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Koribalski\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) discovered a class of diffuse objects with a roundish shape, dubbed \u003Cem class=\"italic\"\u003EOdd Radio Circles\u003C\u002Fem\u003E (ORCs), in the ASKAP EMU pilot survey, that did not correspond to any types of object or artifacts known to have similar morphological features. As it is extremely likely that new discoveries are still waiting to be found in such data deluge, astronomers have started to explore ML-based methods to automatically search for objects with peculiar morphologies. In this process, various methods were proposed, allowing to rediscover previously identified anomalies (including the first detected ORCs) and identify completely new objects (Gupta et al., \u003Ca class=\"xref bibr\" href=\"#ref19\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E; Lochner et al., \u003Ca class=\"xref bibr\" href=\"#ref30\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lochner\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In this context, two major methodologies were used. Gupta et al. (\u003Ca class=\"xref bibr\" href=\"#ref19\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2022\u003C\u002Fa\u003E) and Mostert et al. (\u003Ca class=\"xref bibr\" href=\"#ref37\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Mostert\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) employed rotation and flipping invariant self-organizing maps (SOMs) to search for anomalies in the ASKAP EMU pilot and LOFAR LoTSS survey data, respectively. Both analysis used images of fixed size (approximately 1’ to 5’, \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline88.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline88.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E150 pixels per size), centered around previously catalogued radio sources. The Euclidean distance from each “representative” image in the SOM lattice was used as an “anomaly proxy”, e.g. anomalous images have larger Euclidean distances from their closest SOM template image.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Segal et al. (\u003Ca class=\"xref bibr\" href=\"#ref48\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Segal\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) used a coarse-grained complexity metric as an “anomaly” proxy to detect peculiar objects in the ASKAP EMU pilot survey. Their method is based on the idea that image frames containing complex and anomalous objects have a higher Kolmogorov complexity compared to ordinary frames. In contrast to the previously mentioned methods, Segal et al. (\u003Ca class=\"xref bibr\" href=\"#ref48\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Segal\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) conducted a blind search by sliding fixed image frames of size 256\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline89.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline89.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E256 pixels (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline90.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline90.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E12 arcmin) through the entire map, rather than focusing on frames centered around known source positions. An approximated complexity estimation for each frame was then computed from the compression file size (using the gzip algorithm) of smoothed and resized frames. This allowed the authors to obtain a catalogue of peculiar sources at different reliability levels, corresponding to different complexity threshold choices. The complexity metric is conceptually simple and fast to compute, which is undoubtedly a positive aspect of this method. However, as noted by Mostert et al. (\u003Ca class=\"xref bibr\" href=\"#ref37\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Mostert\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E), the complexity metric may not fully capture the morphological features of the sources present in the images.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E A potential limitation of “source-centric” approaches could be their reliance on catalogues created with traditional source finding algorithms, which are known to have a higher likelihood of missing diffuse sources (a primary target in anomaly searches). Nevertheless, existing studies successfully manage to identify new anomalous sources in their datasets. Mostert et al. (\u003Ca class=\"xref bibr\" href=\"#ref37\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Mostert\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E) also noted that their method is not fully sensitive to detect anomalies at angular scales much smaller than the chosen image size (100 arcsec in their work). The choice of the frame size is an aspect that certainly affects “blind” anomaly searches as well.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f11\" id=\"f11\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig11.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"5188\" height=\"3577\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig11.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 11.\u003C\u002Fspan\u003E Sample images from the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset, labelled as \u003Cspan class=\"monospace\"\u003EPECULIAR\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E. The other assigned labels are reported below each frame. A zscale transform was applied to all images for visualization scopes.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E In this work, we aim to carry out a blind anomaly search study using a different method, which relies on image features extracted by trained self-supervised models. Details on the dataset used and the methodology are provided in the following paragraphs.\u003C\u002Fp\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s5-1\" id=\"s5-1\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E5.1\u003C\u002Fspan\u003E Dataset\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E For this analysis, we considered the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset (55,774 images) described in \u003Ca class=\"xref sec\" href=\"#s2-2\"\u003ESection 2.2\u003C\u002Fa\u003E. We annotated through visual inspection approximately 10% of the data (5800 images) using the following set of labels:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EBACKGROUND\u003C\u002Fspan\u003E: If the image is purely background noise, e.g. no sources are visible. Typically, this label is set for frames located at the map borders;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E: if point sources or compact sources comparable with the synthesized beam size (say \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline91.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline91.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$ \\lt $\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E10 times the beam) are present. Double or triple sources with point-like components also fall into this category;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E: if any extended source is visible, e.g. a compact source with extension \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline92.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline92.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$ \\gt $\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E10 \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline93.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"9\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline93.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\times$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E beam;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003ERADIO-GALAXY\u003C\u002Fspan\u003E: if any extended source is visible with a single- or multi-island morphology, suggesting that of a radio galaxy (e.g. core + lobes);\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EDIFFUSE\u003C\u002Fspan\u003E: if any diffuse source is visible, typically having small-scale (e.g. \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline94.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline94.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$ \\lt $\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003Efew arcmin) and roundish morphology;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EDIFFUSE-LARGE\u003C\u002Fspan\u003E: if any large-scale (e.g. covering half of the image) diffuse object with irregular shape is visible;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EFILAMENT\u003C\u002Fspan\u003E: if any extended filamentary structures is visible;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EARTEFACT\u003C\u002Fspan\u003E: if any ring-shaped or ray-like artefact is visible, e.g. typically around bright resolved sources;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EPECULIAR\u003C\u002Fspan\u003E: if any object is found with peculiar\u002Fanomalous morphology;\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003EMOSAICKING\u003C\u002Fspan\u003E: if any residual pattern of the mosaicking process used to produce the image is present.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E More than one label can be assigned to each image, depending on the object\u002Ffeatures the user recognize in the image.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E A total of 428 peculiar frames were selected through visual inspection starting from a list of 1198 peculiar frames identified in Segal et al. (\u003Ca class=\"xref bibr\" href=\"#ref48\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Segal\u003C\u002Fspan\u003E2023\u003C\u002Fa\u003E) with a complexity metric analysis and from a catalogue of 361 peculiar sources reported in Gupta et al. (\u003Ca class=\"xref bibr\" href=\"#ref17\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Gupta\u003C\u002Fspan\u003E2024\u003C\u002Fa\u003E). In \u003Ca class=\"xref fig\" href=\"#f11\"\u003EFigure 11\u003C\u002Fa\u003E we show examples of peculiar images from the dataset with their annotation labels.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f12\" id=\"f12\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig12.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"4667\" height=\"1969\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig12.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure 12.\u003C\u002Fspan\u003E Left: Anomaly score of frames contained in the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset, shown as black solid histogram, found with the \u003Cem class=\"italic\"\u003EIsolation Forest\u003C\u002Fem\u003E algorithm over top-10 feature data. Unclassified frames are shown with a dashed line. Red filled histogram are the scores of peculiar frames. Ordinary frames (e.g. hosting only compact or artefacts) are shown in blue, pure compact frames in light blue, while frames not tagged as peculiar that host complex sources or structures (\u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EDIFFUSE\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EDIFFUSE-LARGE\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003ERADIO-GALAXY\u003C\u002Fspan\u003E) are shown in green. Right: Anomaly detection metrics (recall, precision, contamination) as a function of the applied anomaly score threshold. Red solid and dashed lines indicate the recall and precision achieved on peculiar frame detection. Purple dotted line is the precision obtained over both peculiar and complex frames. The other solid coloured lines indicate the fraction of unclassified (black line), complex (green line) and ordinary frames contaminating the selected anomaly sample.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s5-2\" id=\"s5-2\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E5.2\u003C\u002Fspan\u003E Anomaly analysis\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E The data representation variables are each sensitive to different features of the images, including details (e.g. the presence of image borders or artifacts, background noise or mosaicking patterns, compact source density, etc) that are not relevant for the anomaly search task. We tried to limit the dependency on background features with the \u003Cem class=\"italic\"\u003ERandomThresholding\u003C\u002Fem\u003E augmentation, but the model was not fully made invariant with respect to the other aspects. For this reason, we carried out a feature selection analysis, aiming to explore and select features that are mostly correlated with the presence of objects with diffuse or extended morphology. We divided the labelled set of images into two groups: “interesting” frames include images labelled as {\u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E,\u003Cspan class=\"monospace\"\u003EDIFFUSE\u003C\u002Fspan\u003E,\u003Cspan class=\"monospace\"\u003EDIFFUSE-LARGE\u003C\u002Fspan\u003E}, while “ordinary” frames include the rest of labelled images, mostly hosting only compact sources or artifacts around them. We then trained a LightGBM\u003Ca class=\"xref fn\" href=\"#fn11\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Ek\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E (Ke et al., \u003Ca class=\"xref bibr\" href=\"#ref25\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Ke\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E) classifier to classify the two groups with all representation features (512) as inputs. A subset of available data was reserved as a cross-validation set for model training early stop. Using shallow decision trees (\u003Cspan class=\"monospace\"\u003Emax_depth\u003C\u002Fspan\u003E=2) and default LightGBM parameters (\u003Cspan class=\"monospace\"\u003Enum_leaves\u003C\u002Fspan\u003E=32, \u003Cspan class=\"monospace\"\u003Emin_data_in_leaf\u003C\u002Fspan\u003E=20), we obtained a classification F1-score of 75.3%. In \u003Ca class=\"xref fig\" href=\"#f14\"\u003EFigure A.2\u003C\u002Fa\u003E we report a plot showing the feature importance returned by the LightGBM trained model. As one can see, a small set of features are identified as the most powerful for selecting interesting frames. We therefore carried out the following data exploration and unsupervised analysis, restricting the parameter set to the top-15 ranked variables in importance.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E In \u003Ca class=\"xref fig\" href=\"#f3\"\u003EFigure 3\u003C\u002Fa\u003E(a) we report a two-dimensional projection of the top-15 variables produced with the UMAP algorithm as a function of the image noise rms level in logarithmic scale (coloured z-axis). As can be seen, the obtained representation shows a residual dependency on physical image parameters, such as the noise rms, that cannot be fully removed by the augmentation scheme currently adopted. In the other panels of \u003Ca class=\"xref fig\" href=\"#f14\"\u003EFigure A.3\u003C\u002Fa\u003E we report the same projection for unlabelled (gray markers) and labelled data, shown with coloured markers. Interestingly, frames that were labelled as peculiar or complex (e.g. containing extended\u002Fdiffuse objects or artifacts) tend to cluster in specific areas of the projected feature space, also related with higher noise areas, while ordinary frames are uniformly spread in the feature space. Other higher noise areas present in \u003Ca class=\"xref fig\" href=\"#f3\"\u003EFigure 3\u003C\u002Fa\u003E(a) seem related to frames that are closer to the mosaic edges or having artifacts (see \u003Ca class=\"xref fig\" href=\"#f3\"\u003EFigure 3\u003C\u002Fa\u003E(b)).\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E We searched for peculiar frames using the \u003Cem class=\"italic\"\u003EIsolation Forest\u003C\u002Fem\u003E (IF) (Liu et al., \u003Ca class=\"xref bibr\" href=\"#ref31\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Liu\u003C\u002Fspan\u003E2008\u003C\u002Fa\u003E) outlier detection algorithm\u003Ca class=\"xref fn\" href=\"#fn12\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003El\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E. We tuned these IF hyperparameters using the annotated dataset:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003Econtamination\u003C\u002Fspan\u003E: The proportion of outliers in the data set. We scanned these values: ‘auto’, 0.001, 0.01, 0.1.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E \n\u003Cspan class=\"monospace\"\u003Emax_samples\u003C\u002Fspan\u003E: The number of samples to draw from the training data to train each base estimator. We scanned these values: ‘auto’, 0.001, 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0.\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E Scans were repeated for different choices of importance ranked feature sets: \u003Cspan class=\"monospace\"\u003Etop2\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003Etop5\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003Etop10\u003C\u002Fspan\u003E, and \u003Cspan class=\"monospace\"\u003Etop15\u003C\u002Fspan\u003E. A number of 200 base estimators were used in the tree ensemble. Other IF parameters were set to defaults. Best classification results were obtained with a smaller fraction of samples (\u003Cspan class=\"monospace\"\u003Emax_samples\u003C\u002Fspan\u003E=0.02) and \u003Cspan class=\"monospace\"\u003Econtamination\u003C\u002Fspan\u003E=0.001.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E We then ran the IF algorithm in an unsupervised way with tuned parameters and obtained an anomaly score for each dataset frame. The anomaly score ranges from 0 to 1, with most anomalous data expected to have values close to 1. In \u003Ca class=\"xref fig\" href=\"#f12\"\u003EFigure 12\u003C\u002Fa\u003E (left panel) we report the distribution of IF anomaly scores of all frames contained in the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset, shown as a black solid histogram, found over top-10 feature data. Unclassified frames are shown with a dashed line. The red filled histogram indicates the labelled peculiar frames. Ordinary frames (e.g. hosting only compact or artifacts) are shown in blue, pure compact frames in light blue, while complex frames (e.g. hosting extended or diffuse structures, not labelled as peculiar) are shown in green.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Following \u003Ca class=\"xref sec\" href=\"#s2-5\"\u003ESection 2.5\u003C\u002Fa\u003E, we computed the anomaly detection metrics (peculiar frame recall and precision, non-peculiar frame contamination) as a function of the applied anomaly score threshold. Peculiar frame recall and precision are reported in \u003Ca class=\"xref fig\" href=\"#f12\"\u003EFigure 12\u003C\u002Fa\u003E (right panel) as a function of the applied anomaly score threshold for top-10 feature data, respectively shown with solid and dashed red lines. We also computed the precision in classifying detected frames as either peculiar or complex, shown with a dotted purple line. The other solid coloured lines indicate the fraction of unclassified (black line), complex (green line) and ordinary frames contaminating the selected anomaly sample. In \u003Ca class=\"xref table\" href=\"#tbl4\"\u003ETable 4\u003C\u002Fa\u003E we summarized the metrics obtained for different feature sets for the anomaly score threshold that provides the best peculiar recall\u002Fprecision compromise (e.g. the score at which recall and precision curves cross in \u003Ca class=\"xref fig\" href=\"#f11\"\u003EFigure 12\u003C\u002Fa\u003E(b)). Best detection performances (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline95.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline95.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E60%) are obtained with the top-5 features, but the top-10 feature set currently provides the smallest contamination fraction of ordinary frames (\u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline96.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"10\" height=\"8\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline96.png\" data-zoomable=\"false\"\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$ \\lt $\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E3%). When considering both peculiar and complex frames, the precision increases to 97%.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cdiv class=\"table-wrap\" data-magellan-destination=\"tbl4\" id=\"tbl4\"\u003E\n\n\u003Cdiv class=\"caption\"\u003E\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003ETable 4.\u003C\u002Fspan\u003E Peculiar frame detection metrics obtained with the \u003Cem class=\"italic\"\u003EIsolation Forest\u003C\u002Fem\u003E algorithm over selected feature sets (column (1)) when using an anomaly score threshold (reported in column (2)) that provides the best compromise in terms of peculiar frame recall and precision, respectively shown in columns (3) and (4). The precision relative to joint peculiar and complex frames is shown in column (5). The fractions of complex and ordinary frames contaminating the predicted anomalous sample are shown in columns (6) and (7).\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cspan\u003E\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab4.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"382\" height=\"133\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_tab4.png\" data-zoomable=\"false\"\u003E\u003C\u002Fdiv\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fdiv\u003E\n\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec\" data-magellan-destination=\"s5-3\" id=\"s5-3\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003E5.3\u003C\u002Fspan\u003E Astronomer-in-the-loop\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E It is worth to note that the source peculiarity concept is rather subjective and may depend on the scientific domain of interest. For instance, a fraction of complex frames may well be considered as truly peculiar in specific analysis, and, on the other hand, missed peculiar frames may be considered not as relevant in other contexts. For this reason, an additional “human-in-the-loop” processing stage has to be applied to our list of candidate anomalies to create a refined sample that better fits scientific needs.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E For the sake of demonstration, we integrated our dataset in the \u003Cspan class=\"monospace\"\u003Eastronomaly\u003C\u002Fspan\u003E package\u003Ca class=\"xref fn\" href=\"#fn13\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Em\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E (Lochner & Bassett, \u003Ca class=\"xref bibr\" href=\"#ref29\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lochner and Bassett\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E). This allowed us to run an active learning process from a web interface in which users can personalize and sort the list of anomalous frames on the basis of the computed score and also their expressed preferences, such as how peculiar a frame is judged on a scale of 1 to 5. A screenshot of the \u003Cspan class=\"monospace\"\u003Eastronomaly\u003C\u002Fspan\u003E UI for our dataset is shown in \u003Ca class=\"xref fig\" href=\"#f16\"\u003EFigure A.4\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E We plan to integrate in the future the full pipeline (feature extraction, anomaly detection, active learning loop) as a supported application within the \u003Cem class=\"italic\"\u003Ecaesar-rest\u003C\u002Fem\u003E service\u003Ca class=\"xref fn\" href=\"#fn14\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003En\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E (Riggi \u003Ca class=\"xref bibr\" href=\"#ref46\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Riggi\u003C\u002Fspan\u003E2021\u003C\u002Fa\u003E), and extend the web UI with missing functionalities (e.g. image filtering\u002Fexporting, model importing, configuration options, etc). In this study, we limited ourselves to primarily quantify the ordinary frame rejection power that can be currently achieved with self-supervised features, as this will largely impact the time needed to visually inspect the anomaly candidates in human-in-the-loop approaches to form the final anomaly sample.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec other\" data-magellan-destination=\"s6\" id=\"s6\"\u003E\n\n\u003Ch2 class=\"A\"\u003E\u003Cspan class=\"label\"\u003E6.\u003C\u002Fspan\u003E Summary\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E In this study, we investigated the potential of self-supervised learning for analysing radio continuum image data produced by SKA precursors. Specifically, we have used the SimCLR contrastive learning framework to train deep network models on large sets of unlabelled images extracted from the ASKAP EMU pilot and SARAO MeerKAT GPS surveys, either randomly selected or centred around catalogued extended source positions. The trained encoder network, based on the \u003Cem class=\"italic\"\u003EResNet18\u003C\u002Fem\u003E architecture, was used as a feature extractor and fine-tuned for three distinct downstream tasks (source detection, morphology classification, and anomaly detection) over test datasets comprising thousands of annotated images from other radio surveys (VLA FIRST, ASKAP Early Science, ATCA Scorpio surveys). Notably, some of these test datasets were purposefully created for this work.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E All trained models, including both the source code and network weights, have been publicly released. These represent a first outcome of this work, as they can be viewed as prototypal radio foundational models, available to be used in future applications for multiple scopes:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E to extract feature parameters from new radio survey images and perform data inspection, unsupervised classification or outlier detection analysis (as demonstrated in \u003Ca class=\"xref sec\" href=\"#s5\"\u003ESection 5\u003C\u002Fa\u003E);\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E to serve as pre-trained backbone components of more complex models designed for source classification, detection or other tasks (e.g. source property characterization), eventually refined over new labelled datasets (as demonstrated in \u003Ca class=\"xref sec\" href=\"#s3\"\u003ESections 3\u003C\u002Fa\u003E and \u003Ca class=\"xref sec\" href=\"#s4\"\u003E4\u003C\u002Fa\u003E).\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E The analyses we performed in this work attempted to address various open questions in this field, paving the way for future analyses:\u003C\u002Fp\u003E\u003Cul class=\"list nomark\"\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Do we observe any advantages stemming from self-supervised models trained on easily constructed “random” survey datasets compared to costly-to-compile “source-centric” datasets?\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E How does self-supervised learning on radio data compare in performance to models pre-trained on extensive non-radio datasets, such as \u003Cem class=\"italic\"\u003EImageNet\u003C\u002Fem\u003E?\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003Cli class=\"list-item\"\u003E\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E•\u003C\u002Fspan\u003E Is it feasible to enhance existing radio source detectors utilizing deep networks through radio self-supervised pre-training?\u003C\u002Fp\u003E\n\u003C\u002Fli\u003E\n\u003C\u002Ful\u003E\n\n\u003Cp class=\"p\"\u003E We found that using uncurated large collections of unlabelled radio images randomly extracted from SKA precursor surveys resulted in significantly improved performances (approximately 5%) in both radio source detection and classification tasks, compared to curated (albeit smaller) image samples extracted around extended source catalogues. This indication, primarily attributed to the augmented number of accessible images achievable with uncurated collections, is highly encouraging, as it suggests that certain aspects of source analysis can be enhanced even without investing numerous work months in catalogue production.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E The advantages gained from self-supervised pre-training on radio data, compared to non-radio data, are notably significant (exceeding 10%) in both source classification and detection tasks. However, when contrasting our findings with fully supervised models trained from scratch, we observed that these benefits are only relevant with small labelled datasets (on the order of a few hundred images). This is certainly a positive aspect, considering that many available annotated datasets (such as \u003Cem class=\"italic\"\u003EMiraBest\u003C\u002Fem\u003E or similar radio galaxy classification datasets) typically fall within this size range. Nevertheless, in order to observe a substantial impact on larger datasets, it becomes imperative to improve both the self-supervised pre-training dataset and the model itself.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E We have identified some areas of developments to be made in the near future to improve source analysis performance, and overcome the limitations encountered in this study. Firstly, we plan to increase the size of our pre-training \u003Cspan class=\"monospace\"\u003Ehulk\u003C\u002Fspan\u003E datasets, by leveraging the massive amount of unlabelled image data being delivered by large area surveys, such as ASKAP EMU, the Very Large Array Sky Survey (VLASS) (Lacy et al., \u003Ca class=\"xref bibr\" href=\"#ref27\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Lacy\u003C\u002Fspan\u003E2020\u003C\u002Fa\u003E), or the LOFAR Two-metre Sky Survey (LoTSS) (Shimwell et al. \u003Ca class=\"xref bibr\" href=\"#ref51\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Shimwell\u003C\u002Fspan\u003E2017\u003C\u002Fa\u003E) surveys. In this context, to reduce the computational load during training, it is crucial to explore effective and automated strategies for constructing semi-curated large-scale pre-training datasets, potentially comprising millions of images. This step may require the development of specialized algorithms to filter or weight image frames included in the pre-training dataset, aiming to maximize the balance between ordinary and complex objects “seen” by the model.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E Additionally, we have already started to train larger architectures and recent state-of-the-art self-supervised frameworks, particularly those based on Vision Transformers (ViTs), over the same datasets produced for this study. Results will be compared against the SimCLR baseline and presented in a forthcoming paper.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"back\"\u003E\n\u003Cdiv class=\"ack\"\u003E\n\u003Ch2 class=\"A\"\u003E Acknowledgement\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E This scientific work uses data obtained from Inyarrimanha Ilgari Bundara\u002Fthe Murchison Radio-astronomy Observatory. We acknowledge the Wajarri Yamaji People as the Traditional Owners and native title holders of the Observatory site. CSIRO’s ASKAP radio telescope is part of the Australia Telescope National Facility (\u003Ca class=\"uri\" href=\"https:\u002F\u002Fror.org\u002F05qajvd42\"\u003Ehttps:\u002F\u002Fror.org\u002F05qajvd42\u003C\u002Fa\u003E). Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing Research Centre. Establishment of ASKAP, Inyarrimanha Ilgari Bundara, the CSIRO Murchison Radio-astronomy Observatory and the Pawsey Supercomputing Research Centre are initiatives of the Australian Government, with support from the Government of Western Australia and the Science and Industry Endowment Fund.\u003C\u002Fp\u003E\n\u003Cp class=\"p\"\u003E This work made use of PLEIADI, a computing infrastructure installed and managed by INAF.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec other\" data-magellan-destination=\"s50\" id=\"s50\"\u003E\n\u003Ch2 class=\"A\"\u003E Funding statement\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E This work received funding from the INAF CIRASA and SCIARADA projects.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec coi-statement\" data-magellan-destination=\"s51\" id=\"s51\"\u003E\n\u003Ch2 class=\"A\"\u003E Competing interests\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E None.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"sec data-availability\" data-magellan-destination=\"s52\" id=\"s52\"\u003E\n\u003Ch2 class=\"A\"\u003E Data availability statement\u003C\u002Fh2\u003E\n\u003Cp class=\"p\"\u003E The software code used in this work is publicly available under the GNU General Public License v3.0\u003Ca class=\"xref fn\" href=\"#fn15\"\u003E\u003Cspan class=\"show-for-sr\"\u003EFootnote \u003C\u002Fspan\u003E\n\u003Csup class=\"sup\"\u003Eo\u003C\u002Fsup\u003E\n\u003C\u002Fa\u003E on the GitHub repository \u003Ca class=\"uri\" href=\"https:\u002F\u002Fgithub.com\u002FSKA-INAF\u002Fsclassifier\u002F\"\u003Ehttps:\u002F\u002Fgithub.com\u002FSKA-INAF\u002Fsclassifier\u002F\u003C\u002Fa\u003E. The trained model weights have been made available on Zenodo repository at \u003Ca class=\"uri\" href=\"https:\u002F\u002Fdoi.org\u002F10.5281\u002Fzenodo.12636593\"\u003Ehttps:\u002F\u002Fdoi.org\u002F10.5281\u002Fzenodo.12636593\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\n\n\n\u003Cdiv class=\"app-group\" data-magellan-destination=\"appg1\" id=\"appg1\"\u003E\n\u003Ch2 class=\"A\"\u003EAppendix\u003C\u002Fh2\u003E\n\u003Cdiv class=\"app\" data-magellan-destination=\"app1\" id=\"app1\"\u003E\n\n\u003Ch3 class=\"B\"\u003E\u003Cspan class=\"label\"\u003EA.\u003C\u002Fspan\u003E Supplementary plots\u003C\u002Fh3\u003E\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f13\" id=\"f13\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig13.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"5189\" height=\"3508\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig13.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure A.1.\u003C\u002Fspan\u003E Examples of sources from the RGZ test dataset that were misclassified by the trained source classifier (\u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E pre-trained and frozen backbone model) due to an incorrect true class label provided in the dataset (mislabelling). The true and predicted class labels are reported below each frame. In many cases, the model indeed correctly predicted the expected true classification (denoted as “true corr.” below each frame).\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f14\" id=\"f14\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig14.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"2427\" height=\"1598\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig14.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure A.2.\u003C\u002Fspan\u003E Feature importance obtained with a LightGBM classifier trained on \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E data representation, for the classification of interesting against ordinary images.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f15\" id=\"f15\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig15.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"4375\" height=\"4175\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig15.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure A.3.\u003C\u002Fspan\u003E Figure 14: 2D UMAP projection of the top-15 selected features from the data representation vector produced by the trained SimCLR model on the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset as a function of the image noise RMS level in logarithmic scale (z-scale axis). Red markers correspond to image with higher RMS levels, while blue markers to low noise RMS levels. Left: 2D UMAP projection of the top-15 selected features for unclassified frames (gray markers) and labelled frames (coloured markers, as reported in the plot legends). See text for details on label schema.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Csection\u003E\u003Cdiv class=\"fig\" data-magellan-destination=\"f16\" id=\"f16\"\u003E\n\n\n\u003Cdiv class=\"figure-thumb\"\u003E\u003Cimg src=\"data:image\u002Fgif;base64,R0lGODlhAQABAIAAAMLCwgAAACH5BAAAAAAALAAAAAABAAEAAAICRAEAOw==\" data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig16.png?pub-status=live\" class=\"aop-lazy-load-image\" width=\"5187\" height=\"2991\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_fig16.png\" data-zoomable=\"true\"\u003E\u003C\u002Fdiv\u003E\n\u003Cdiv class=\"caption\"\u003E\u003Cp class=\"p\"\u003E \n\u003C\u002Fp\u003E\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003EFigure A.4.\u003C\u002Fspan\u003E Screenshot of \u003Cspan class=\"monospace\"\u003Eastronomaly\u003C\u002Fspan\u003E web UI with list of anomalous frames selected from the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset.\u003C\u002Fp\u003E\n\u003C\u002Fdiv\u003E\u003C\u002Fdiv\u003E\u003C\u002Fsection\u003E\n\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E\n\u003C\u002Fdiv\u003E",tableOfContent:[{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EIntroduction\u003C\u002Fdiv\u003E",url:"s1"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003ESelf-supervised learning of radio data\u003C\u002Fdiv\u003E",url:"s2"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003ETask I: Classification of radio source morphology\u003C\u002Fdiv\u003E",url:"s3"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003ETask II: Radio source detection\u003C\u002Fdiv\u003E",url:"s4"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003ETask III: Search for peculiar objects\u003C\u002Fdiv\u003E",url:"s5"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003ESummary\u003C\u002Fdiv\u003E",url:"s6"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EFunding statement\u003C\u002Fdiv\u003E",url:"s50"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003ECompeting interests\u003C\u002Fdiv\u003E",url:"s51"},{level:k,current:b,title:"\u003Cdiv class=\"toc-title\"\u003EData availability statement\u003C\u002Fdiv\u003E",url:"s52"}],footnotes:[],fulltextNotes:[{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003E\n\u003Csup class=\"sup\"\u003Ea\u003C\u002Fsup\u003E\n\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E \n\u003Ca class=\"uri\" href=\"https:\u002F\u002Fwww.zooniverse.org\u002Fprojects\u002Fchrismrp\u002Fradio-galaxy-zoo-lofar\"\u003Ehttps:\u002F\u002Fwww.zooniverse.org\u002Fprojects\u002Fchrismrp\u002Fradio-galaxy-zoo-lofar\u003C\u002Fa\u003E\n\u003C\u002Fp\u003E\n",targetId:"fn1",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Eb\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E \n\u003Ca class=\"uri\" href=\"https:\u002F\u002Fwww.zooniverse.org\u002Fprojects\u002Fhongming-tang\u002Fradio-galaxy-zoo-emu\"\u003Ehttps:\u002F\u002Fwww.zooniverse.org\u002Fprojects\u002Fhongming-tang\u002Fradio-galaxy-zoo-emu\u003C\u002Fa\u003E\n\u003C\u002Fp\u003E\n",targetId:"fn2",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Ec\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E The observed metric differences between BYOL and SimCLR pre-trained models are not significant (below 1%) given the reported uncertainties.\u003C\u002Fp\u003E\n",targetId:"fn3",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Ed\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E Out of \u003Cspan data-mathjax-status=\"alt-graphic\" class=\"inline-formula\"\u003E\n\u003Cspan class=\"alternatives\"\u003E\n\u003Cimg data-src=\"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline35.png?pub-status=live\" class=\"aop-lazy-load-image mathjax-alternative mathjax-alt-graphic mathjax-off\" width=\"12\" height=\"4\" data-original-image=\"\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary:20241104170759220-0615:S1323358024000845:S1323358024000845_inline35.png\" data-zoomable=\"false\" \u002F\u003E\n\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E\n$\\sim$\n\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E\n\u003C\u002Fspan\u003E5 800 catalogued sources that were labelled as candidate radio galaxies on the basis of their radio morphology, only one was found to have a size (7.4’) larger than the chosen image cutout (6.4’).\u003C\u002Fp\u003E\n",targetId:"fn4",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Ee\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E Wide-angle tail\u003C\u002Fp\u003E\n",targetId:"fn5",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Ef\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E narrow-angle tail\u003C\u002Fp\u003E\n",targetId:"fn6",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Eg\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E The RGZ project is a crowdsourced science project where both scientists and citizens can classify radio galaxies and their host galaxies from radio and infrared (WISE survey, Wright et al. \u003Ca class=\"xref bibr\" href=\"#ref57\"\u003E\u003Cspan class=\"show-for-sr\"\u003EReference Wright\u003C\u002Fspan\u003E2010\u003C\u002Fa\u003E) images presented to users in a web interface\u003C\u002Fp\u003E\n",targetId:"fn7",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Eh\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E When mentioning the \u003Cspan class=\"monospace\"\u003EImageNet\u003C\u002Fspan\u003E dataset throughout the paper, we refer to the \u003Cspan class=\"monospace\"\u003EImageNet-1k\u003C\u002Fspan\u003E version.\u003C\u002Fp\u003E\n",targetId:"fn8",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Ei\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E \n\u003Ca class=\"uri\" href=\"https:\u002F\u002Fgithub.com\u002FSKA-INAF\u002Fcaesar-mrcnn-tf2\"\u003Ehttps:\u002F\u002Fgithub.com\u002FSKA-INAF\u002Fcaesar-mrcnn-tf2\u003C\u002Fa\u003E\n\u003C\u002Fp\u003E\n",targetId:"fn9",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Ej\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E In astronomical source catalogue works, the recall\u002Fprecision metrics are often referred to as completeness\u002Freliability.\u003C\u002Fp\u003E\n",targetId:"fn10",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Ek\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E LightGBM is a high-performance gradient boosting framework based on decision tree algorithm, particularly suited for classification tasks on tabular data. More details are available at \u003Ca class=\"uri\" href=\"https:\u002F\u002Flightgbm.readthedocs.io\u002Fen\u002Flatest\u002Findex.html\"\u003Ehttps:\u002F\u002Flightgbm.readthedocs.io\u002Fen\u002Flatest\u002Findex.html\u003C\u002Fa\u003E.\u003C\u002Fp\u003E\n",targetId:"fn11",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003El\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E \n\u003Cem class=\"italic\"\u003EIsolation Forest\u003C\u002Fem\u003E is an unsupervised decision-tree-based algorithm for outlier detection in tabular data, that works by randomly selecting a feature and a random split value to isolate data points in a binary tree. It identifies outliers as instances that require fewer splits to be isolated, exploiting the inherent rarity of anomalies in a dataset.\u003C\u002Fp\u003E\n",targetId:"fn12",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Em\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E \n\u003Ca class=\"uri\" href=\"https:\u002F\u002Fgithub.com\u002FMichelleLochner\u002Fastronomaly\"\u003Ehttps:\u002F\u002Fgithub.com\u002FMichelleLochner\u002Fastronomaly\u003C\u002Fa\u003E\n\u003C\u002Fp\u003E\n",targetId:"fn13",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003En\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E \n\u003Ca class=\"uri\" href=\"https:\u002F\u002Fgithub.com\u002FSKA-INAF\u002Fcaesar-rest\"\u003Ehttps:\u002F\u002Fgithub.com\u002FSKA-INAF\u002Fcaesar-rest\u003C\u002Fa\u003E\n\u003C\u002Fp\u003E\n",targetId:"fn14",displayNumber:a},{content:"\n\n\u003Cp class=\"p\"\u003E\u003Cspan class=\"label\"\u003E\n\u003Csup class=\"sup\"\u003Eo\u003C\u002Fsup\u003E\n\u003C\u002Fspan\u003E \n\u003Ca class=\"uri\" href=\"https:\u002F\u002Fwww.gnu.org\u002Flicenses\u002Fgpl-3.0.html\"\u003Ehttps:\u002F\u002Fwww.gnu.org\u002Flicenses\u002Fgpl-3.0.html\u003C\u002Fa\u003E\n\u003C\u002Fp\u003E\n",targetId:"fn15",displayNumber:a}],references:[{id:"ref1",displayNumber:a,existInContent:c,content:"\u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EAniyan\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EA. K.\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, & \u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EThorat\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EK.\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E \u003Cspan class=\"year\"\u003E2017\u003C\u002Fspan\u003E, \u003Cspan class=\"source\"\u003EApJS\u003C\u002Fspan\u003E, 230, \u003Cspan class=\"fpage\"\u003E20\u003C\u002Fspan\u003E\n\u003Ca class='ref-link' target='_blank' aria-label='CrossRef link for Aniyan, A. K., & Thorat, K. 2017, ApJS, 230, 20' href=https:\u002F\u002Fdx.doi.org\u002F10.3847\u002F1538-4365\u002Faa7333\u003ECrossRef\u003C\u002Fa\u003E\u003Ca class='ref-link' target='_blank' aria-label='Google Scholar link for Aniyan, A. 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L., et al. 2010, AJ, 140, 1868",doi:a,crossRefLink:a,pubMedLink:a}]},{id:"ref58",displayNumber:a,existInContent:c,content:"\u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EWu\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EC.\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"etal\"\u003Eet al.\u003C\u002Fspan\u003E \u003Cspan class=\"year\"\u003E2019\u003C\u002Fspan\u003E, \u003Cspan class=\"source\"\u003EMNRAS\u003C\u002Fspan\u003E, 482, \u003Cspan class=\"fpage\"\u003E1211\u003C\u002Fspan\u003E\n\u003Ca class='ref-link' target='_blank' aria-label='Google Scholar link for Wu, C., et al. 2019, MNRAS, 482, 1211' href=https:\u002F\u002Fscholar.google.com\u002Fscholar?q=Wu,+C.,+et+al.+2019,+MNRAS,+482,+1211\u003EGoogle Scholar\u003C\u002Fa\u003E",item:[{googleScholarLink:"https:\u002F\u002Fscholar.google.com\u002Fscholar?q=Wu,+C.,+et+al.+2019,+MNRAS,+482,+1211",openUrlParams:{genre:g,date:s,sid:f,title:d},innerRefId:"r58",title:"Wu, C., et al. 2019, MNRAS, 482, 1211",doi:a,crossRefLink:a,pubMedLink:a}]},{id:"ref59",displayNumber:a,existInContent:c,content:"\u003Cspan class=\"string-name\"\u003E\u003Cspan class=\"surname\"\u003EZhang\u003C\u002Fspan\u003E, \u003Cspan class=\"given-names\"\u003EZ.\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E, \u003Cspan class=\"etal\"\u003Eet al.\u003C\u002Fspan\u003E \u003Cspan class=\"year\"\u003E2022\u003C\u002Fspan\u003E, \u003Cspan class=\"source\"\u003EPASP\u003C\u002Fspan\u003E, 134, \u003Cspan class=\"fpage\"\u003E064503\u003C\u002Fspan\u003E\n\u003Ca class='ref-link' target='_blank' aria-label='CrossRef link for Zhang, Z., et al. 2022, PASP, 134, 064503' href=https:\u002F\u002Fdx.doi.org\u002F10.1088\u002F1538-3873\u002Fac67b1\u003ECrossRef\u003C\u002Fa\u003E\u003Ca class='ref-link' target='_blank' aria-label='Google Scholar link for Zhang, Z., et al. 2022, PASP, 134, 064503' href=https:\u002F\u002Fscholar.google.com\u002Fscholar?q=Zhang,+Z.,+et+al.+2022,+PASP,+134,+064503\u003EGoogle Scholar\u003C\u002Fa\u003E",item:[{googleScholarLink:"https:\u002F\u002Fscholar.google.com\u002Fscholar?q=Zhang,+Z.,+et+al.+2022,+PASP,+134,+064503",openUrlParams:{genre:g,date:m,sid:f,title:d},innerRefId:"r59",title:"Zhang, Z., et al. 2022, PASP, 134, 064503",doi:"10.1088\u002F1538-3873\u002Fac67b1",crossRefLink:"https:\u002F\u002Fdx.doi.org\u002F10.1088\u002F1538-3873\u002Fac67b1",pubMedLink:a}]}],figures:[{contentId:"f1",label:"Figure 1.",description:"\u003Cspan class=\"p\"\u003ESchema of self-supervised learning for radio data analysis.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-17399-mediumThumb-png-S1323358024000845_fig1.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-98255-optimisedImage-png-S1323358024000845_fig1.jpg",attrib:[]},{contentId:"tbl1",label:"Table 1.",description:"\u003Cspan class=\"p\"\u003ESummary information of datasets used for SimCLR model training. The number of images \u003Cspan class=\"alternatives\"\u003E\u003Cimg class=\"inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off\" data-mimesubtype=\"png\" data-type src=\"${staticDomain}\u002Fcontent\u002Fid\u002Furn:cambridge.org:id:article:S1323358024000845\u002Fresource\u002Fname\u002FS1323358024000845_inline47.png?pub-status=live\" \u002F\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$n_{img}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E is reported in column (2). The image size \u003Cspan class=\"alternatives\"\u003E\u003Cimg class=\"inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off\" data-mimesubtype=\"png\" data-type src=\"${staticDomain}\u002Fcontent\u002Fid\u002Furn:cambridge.org:id:article:S1323358024000845\u002Fresource\u002Fname\u002FS1323358024000845_inline48.png?pub-status=live\" \u002F\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$s_{img}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E is reported in column (3). \u003Cspan class=\"alternatives\"\u003E\u003Cimg class=\"inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off\" data-mimesubtype=\"png\" data-type src=\"${staticDomain}\u002Fcontent\u002Fid\u002Furn:cambridge.org:id:article:S1323358024000845\u002Fresource\u002Fname\u002FS1323358024000845_inline49.png?pub-status=live\" \u002F\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$s_{img}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E is fixed for all images in the \u003Cspan class=\"monospace\"\u003Ehulk_smgp\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E datasets, while \u003Cspan class=\"alternatives\"\u003E\u003Cimg class=\"inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off\" data-mimesubtype=\"png\" data-type src=\"${staticDomain}\u002Fcontent\u002Fid\u002Furn:cambridge.org:id:article:S1323358024000845\u002Fresource\u002Fname\u002FS1323358024000845_inline50.png?pub-status=live\" \u002F\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$s_{img}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E is not fixed and depends on the source size \u003Cspan class=\"alternatives\"\u003E\u003Cimg class=\"inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off\" data-mimesubtype=\"png\" data-type src=\"${staticDomain}\u002Fcontent\u002Fid\u002Furn:cambridge.org:id:article:S1323358024000845\u002Fresource\u002Fname\u002FS1323358024000845_inline51.png?pub-status=live\" \u002F\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$s_{\\text{source}}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E (equivalent to the maximum source bounding box dimension) in the \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E datasets. For these datasets, we report the average, minimum and maximum source sizes in columns (4), (5) and (6), respectively. Images from all datasets are eventually resized to a fixed size for model training and testing (see Section 2.3).\u003C\u002Fspan\u003E",thumbnailSrc:U,enlargedSrc:U,attrib:[]},{contentId:"f2",label:"Figure 2.",description:"\u003Cspan class=\"p\"\u003ERepresentative examples of images from the \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (top panels), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (middle panels) and \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (bottom panels) datasets. A zscale transform was applied to all images for visualization scopes. Top panels: sample images containing only compact sources (Figure 2(a)), or multiple extended sources (Figures 2(b) and 2(c)). Middle panels: sample source with diffuse morphology (Figure 2(d)), a multi-component extended source exhibiting typical radio galaxy morphology (Figure 2(e)), a single-component extended source with a roundish morphology (Figure 2(f)). Bottom panels: sample sources with FR-I (Figure 2(g)), FR-II (Figure 2(h)) and peculiar (Figure 2(i)) classification.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-65434-mediumThumb-png-S1323358024000845_fig2.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-82944-optimisedImage-png-S1323358024000845_fig2.jpg",attrib:[]},{contentId:"tbl2",label:"Table 2.",description:"\u003Cspan class=\"p\"\u003EList of augmentations used in SimCLR model training. In column (2) we reported the transform parameter values. In column (3) we reported the probability used to apply the transform in the augmentation pipeline, e.g. 1.0 means the transform is always applied to all input images.\u003C\u002Fspan\u003E",thumbnailSrc:V,enlargedSrc:V,attrib:[]},{contentId:"tbl3",label:"Table 3.",description:"\u003Cspan class=\"p\"\u003EList of hyperparameters used in SimCLR model training.\u003C\u002Fspan\u003E",thumbnailSrc:W,enlargedSrc:W,attrib:[]},{contentId:"f3",label:"Figure 3.",description:"\u003Cspan class=\"p\"\u003ESample images from the RGZ dataset with representative sources of different morphological classes (reported below each frame). A zscale transform was applied to all images for visualization scopes.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-89259-mediumThumb-png-S1323358024000845_fig3.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-13619-optimisedImage-png-S1323358024000845_fig3.jpg",attrib:[]},{contentId:"f4",label:"Figure 4.",description:"\u003Cspan class=\"p\"\u003E2D UMAP projection of the data representation vector (size = 512) produced by the trained \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E model on the RGZ dataset.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-73742-mediumThumb-png-S1323358024000845_fig4.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-30709-optimisedImage-png-S1323358024000845_fig4.jpg",attrib:[]},{contentId:"f5",label:"Figure 5.",description:"\u003Cspan class=\"p\"\u003EClassification F1-scores obtained for different classes and for all classes cumulatively over RGZ test sets with different pre-trained and frozen backbone models: \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (red squares), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (blue inverted triangles), \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E (green triangles), \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (orange diamonds), \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E (cyan asterisks), \u003Cspan class=\"monospace\"\u003EImageNet\u003C\u002Fspan\u003E (black dots). The reported values and errors are the F1-score mean and mean error computed over five test sets.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-68307-mediumThumb-png-S1323358024000845_fig5.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-95705-optimisedImage-png-S1323358024000845_fig5.jpg",attrib:[]},{contentId:"f6",label:"Figure 6.",description:"\u003Cspan class=\"p\"\u003EConfusion matrix of the source morphology classifier (trained with \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E pre-trained and frozen backbone model) obtained over the RGZ test set.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-17641-mediumThumb-png-S1323358024000845_fig6.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-01879-optimisedImage-png-S1323358024000845_fig6.jpg",attrib:[]},{contentId:"f7",label:"Figure 7.",description:"\u003Cspan class=\"p\"\u003EClassification F1-scores obtained (for all classes cumulatively) over RGZ test sets as a function of the number of images \u003Cspan class=\"alternatives\"\u003E\u003Cimg class=\"inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off\" data-mimesubtype=\"png\" data-type src=\"${staticDomain}\u002Fcontent\u002Fid\u002Furn:cambridge.org:id:article:S1323358024000845\u002Fresource\u002Fname\u002FS1323358024000845_inline85.png?pub-status=live\" \u002F\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$n_{train}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E in the training set with two alternative models: one trained from scratch (open black dots), the other trained with backbone model weights initialized to \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E weights (filled black dots). The upper x-axis indicates the fraction of the full training set considered in each training run.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-63009-mediumThumb-png-S1323358024000845_fig7.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-99012-optimisedImage-png-S1323358024000845_fig7.jpg",attrib:[]},{contentId:"f8",label:"Figure 8.",description:"\u003Cspan class=\"p\"\u003ESample images (taken from Riggi 2023) from the dataset used for \u003Cspan class=\"italic\"\u003Ecaesar-mrcnn\u003C\u002Fspan\u003E training\u002Ftesting, including objects of different classes: a \u003Cspan class=\"monospace\"\u003EFLAGGED\u003C\u002Fspan\u003E object (Figure 8(a), in gray), \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E objects (in blue), a \u003Cspan class=\"monospace\"\u003EMULTI-ISLAND\u003C\u002Fspan\u003E object (Figure 8(b), in orange), \u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E objects (Figure 8(c), in yellow), \u003Cspan class=\"monospace\"\u003ESPURIOUS\u003C\u002Fspan\u003E objects (Figure 8(d), in red).\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-87738-mediumThumb-png-S1323358024000845_fig8.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-36452-optimisedImage-png-S1323358024000845_fig8.jpg",attrib:[]},{contentId:"f9",label:"Figure 9.",description:"\u003Cspan class=\"p\"\u003EMask R-CNN object detection F1-score metric obtained for different object classes over multiple test sets with different pre-trained and frozen backbone models: \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E (red squares), \u003Cspan class=\"monospace\"\u003Ebanner_smgps\u003C\u002Fspan\u003E (blue iverted triangles), \u003Cspan class=\"monospace\"\u003Esmart_hulk_smgps\u003C\u002Fspan\u003E (green triangles), \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E (orange diamonds), \u003Cspan class=\"monospace\"\u003Ebanner_emupilot\u003C\u002Fspan\u003E (cyan asterisks), \u003Cspan class=\"monospace\"\u003EImageNet\u003C\u002Fspan\u003E (black dots). The reported values and errors are the means and mean errors computed over 5 test sets.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-16536-mediumThumb-png-S1323358024000845_fig9.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-90428-optimisedImage-png-S1323358024000845_fig9.jpg",attrib:[]},{contentId:"f10",label:"Figure 10.",description:"\u003Cspan class=\"p\"\u003EMask R-CNN object detection F1-score metric obtained over the \u003Cspan class=\"monospace\"\u003ESOURCE\u003C\u002Fspan\u003E class over multiple test sets as a function of the number of images \u003Cspan class=\"alternatives\"\u003E\u003Cimg class=\"inline-graphic mathjax-alternative mathjax-alt-graphic mathjax-off\" data-mimesubtype=\"png\" data-type src=\"${staticDomain}\u002Fcontent\u002Fid\u002Furn:cambridge.org:id:article:S1323358024000845\u002Fresource\u002Fname\u002FS1323358024000845_inline87.png?pub-status=live\" \u002F\u003E\u003Cspan class=\"mathjax-tex-wrapper\" data-mathjax-type=\"texmath\"\u003E\u003Cspan class=\"tex-math mathjax-tex-math mathjax-on\"\u003E$n_{train}$\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E\u003C\u002Fspan\u003E in the training set with two alternative models: one trained from scratch (open markers), the other trained with backbone model weights initialized to \u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E weights (filled markers). The upper x-axis indicates the fraction of the full training set considered in each training run.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-69728-mediumThumb-png-S1323358024000845_fig10.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-97907-optimisedImage-png-S1323358024000845_fig10.jpg",attrib:[]},{contentId:"f11",label:"Figure 11.",description:"\u003Cspan class=\"p\"\u003ESample images from the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset, labelled as \u003Cspan class=\"monospace\"\u003EPECULIAR\u003C\u002Fspan\u003E and \u003Cspan class=\"monospace\"\u003ECOMPACT\u003C\u002Fspan\u003E. The other assigned labels are reported below each frame. A zscale transform was applied to all images for visualization scopes.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-69911-mediumThumb-png-S1323358024000845_fig11.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-74419-optimisedImage-png-S1323358024000845_fig11.jpg",attrib:[]},{contentId:"f12",label:"Figure 12.",description:"\u003Cspan class=\"p\"\u003ELeft: Anomaly score of frames contained in the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset, shown as black solid histogram, found with the \u003Cspan class=\"italic\"\u003EIsolation Forest\u003C\u002Fspan\u003E algorithm over top-10 feature data. Unclassified frames are shown with a dashed line. Red filled histogram are the scores of peculiar frames. Ordinary frames (e.g. hosting only compact or artefacts) are shown in blue, pure compact frames in light blue, while frames not tagged as peculiar that host complex sources or structures (\u003Cspan class=\"monospace\"\u003EEXTENDED\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EDIFFUSE\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003EDIFFUSE-LARGE\u003C\u002Fspan\u003E, \u003Cspan class=\"monospace\"\u003ERADIO-GALAXY\u003C\u002Fspan\u003E) are shown in green. Right: Anomaly detection metrics (recall, precision, contamination) as a function of the applied anomaly score threshold. Red solid and dashed lines indicate the recall and precision achieved on peculiar frame detection. Purple dotted line is the precision obtained over both peculiar and complex frames. The other solid coloured lines indicate the fraction of unclassified (black line), complex (green line) and ordinary frames contaminating the selected anomaly sample.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-37535-mediumThumb-png-S1323358024000845_fig12.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-03853-optimisedImage-png-S1323358024000845_fig12.jpg",attrib:[]},{contentId:"tbl4",label:"Table 4.",description:"\u003Cspan class=\"p\"\u003EPeculiar frame detection metrics obtained with the \u003Cspan class=\"italic\"\u003EIsolation Forest\u003C\u002Fspan\u003E algorithm over selected feature sets (column (1)) when using an anomaly score threshold (reported in column (2)) that provides the best compromise in terms of peculiar frame recall and precision, respectively shown in columns (3) and (4). The precision relative to joint peculiar and complex frames is shown in column (5). The fractions of complex and ordinary frames contaminating the predicted anomalous sample are shown in columns (6) and (7).\u003C\u002Fspan\u003E",thumbnailSrc:X,enlargedSrc:X,attrib:[]},{contentId:"f13",label:"Figure A.1.",description:"\u003Cspan class=\"p\"\u003EExamples of sources from the RGZ test dataset that were misclassified by the trained source classifier (\u003Cspan class=\"monospace\"\u003Ehulk_smgps\u003C\u002Fspan\u003E pre-trained and frozen backbone model) due to an incorrect true class label provided in the dataset (mislabelling). The true and predicted class labels are reported below each frame. In many cases, the model indeed correctly predicted the expected true classification (denoted as “true corr.” below each frame).\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-02897-mediumThumb-png-S1323358024000845_fig13.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-59184-optimisedImage-png-S1323358024000845_fig13.jpg",attrib:[]},{contentId:"f14",label:"Figure A.2.",description:"\u003Cspan class=\"p\"\u003EFeature importance obtained with a LightGBM classifier trained on \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E data representation, for the classification of interesting against ordinary images.\u003C\u002Fspan\u003E",thumbnailSrc:Y,enlargedSrc:Y,attrib:[]},{contentId:"f15",label:"Figure A.3.",description:"\u003Cspan class=\"p\"\u003EFigure 14: 2D UMAP projection of the top-15 selected features from the data representation vector produced by the trained SimCLR model on the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset as a function of the image noise RMS level in logarithmic scale (z-scale axis). Red markers correspond to image with higher RMS levels, while blue markers to low noise RMS levels. Left: 2D UMAP projection of the top-15 selected features for unclassified frames (gray markers) and labelled frames (coloured markers, as reported in the plot legends). See text for details on label schema.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-70422-mediumThumb-png-S1323358024000845_fig15.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-11677-optimisedImage-png-S1323358024000845_fig15.jpg",attrib:[]},{contentId:"f16",label:"Figure A.4.",description:"\u003Cspan class=\"p\"\u003EScreenshot of \u003Cspan class=\"monospace\"\u003Eastronomaly\u003C\u002Fspan\u003E web UI with list of anomalous frames selected from the \u003Cspan class=\"monospace\"\u003Ehulk_emupilot\u003C\u002Fspan\u003E dataset.\u003C\u002Fspan\u003E",thumbnailSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-44984-mediumThumb-png-S1323358024000845_fig16.jpg",enlargedSrc:"https:\u002F\u002Fstatic.cambridge.org\u002Fbinary\u002Fversion\u002Fid\u002Furn:cambridge.org:id:binary-alt:20241104171006-37754-optimisedImage-png-S1323358024000845_fig16.jpg",attrib:[]}]},pdf:{standardResolution:{fileUrl:"\u002Fcore\u002Fservices\u002Faop-cambridge-core\u002Fcontent\u002Fview\u002FE4F61E099F4092E9229652B4BB68DD41\u002FS1323358024000845a.pdf\u002Fself-supervised-contrastive-learning-of-radio-data-for-source-detection-classification-and-peculiar-object-discovery.pdf",fileSizeInMb:3,articleTitle:v,slugTitle:"self-supervised-contrastive-learning-of-radio-data-for-source-detection-classification-and-peculiar-object-discovery"},highResolution:d,media:d},classification:[],supplementaryMaterials:[],relations:{corrections:[],correctionsOriginals:[],retractions:[],retractionsOriginals:[],addendums:[],addendumsOriginals:[],hasAnyRelations:b,hasAnyOriginalArticle:b},settings:{hasAccess:c,isOpenAccess:b,displayRightsLink:c,shouldDisplayCrossMark:c,shouldDisplayNasaAds:c,suppressPdf:b,isShareable:c,isAnnotationsEnabled:b,disableArticleCommentary:b,displayArticleCommentaryAsDiscussionLinks:b,isCommentsEnabled:b,hasContent:c,shouldDisplaySubmitContent:b,isResearchDirections:b,isQuestionCollection:b,isMathjaxEnabled:c},citationCount:z,openUrlParams:"?genre=article&atitle=Self-supervised%20contrastive%20learning%20of%20radio%20data%20for%20source%20detection%2C%20classification%20and%20peculiar%20object%20discovery&jtitle=Publications%20of%20the%20Astronomical%20Society%20of%20Australia&title=Publications%20of%20the%20Astronomical%20Society%20of%20Australia&date=2024&volume=41&artnum=e085&sid=https%3A%2F%2Fwww.cambridge.org%2Fcore&aulast=Riggi&aufirst=S.&doi=10.1017\u002Fpasa.2024.84",ecommerceProducts:{digitalSku:n,paperBackSku:d,hardBackSku:d},subject:[],permissionUrl:"https:\u002F\u002Fs100.copyright.com\u002FAppDispatchServlet?publisherName=CUP&publication=PAS&title=Self-supervised%20contrastive%20learning%20of%20radio%20data%20for%20source%20detection%2C%20classification%20and%20peculiar%20object%20discovery&publicationDate=05%20November%202024&author=S.%20Riggi%2C%20T.%20Cecconello%2C%20S.%20Palazzo%2C%20A.M.%20Hopkins%2C%20N.%20Gupta%2C%20C.%20Bordiu%2C%20A.%20Ingallinera%2C%20C.%20Buemi%2C%20F.%20Bufano%2C%20F.%20Cavallaro%2C%20M.D.%20Filipovi%C4%87%2C%20P.%20Leto%2C%20S.%20Loru%2C%20A.C.%20Ruggeri%2C%20C.%20Trigilio%2C%20G.%20Umana%2C%20F.%20Vitello&copyright=%C2%A9%20The%20Author(s)%2C%202024.%20Published%20by%20Cambridge%20University%20Press%20on%20behalf%20of%20Astronomical%20Society%20of%20Australia&contentID=10.1017%2Fpasa.2024.84&startPage=&endPage=&orderBeanReset=True&volumeNum=41&issueNum=&oa="},breadcrumbs:[{name:"Home",url:"\u002Fcore"},{name:"Journals",url:"\u002Fcore\u002Fpublications\u002Fjournals"},{name:p,url:F},{name:G,url:H},{name:"Self-supervised 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0-1.385l3.352-3.328-3.352-3.33a.983.983 0 0 1 0-1.384 1 1 0 0 1 1.395 0l3.352 3.329 3.352-3.329a1 1 0 0 1 1.394 0 .983.983 0 0 1 0 1.385l-3.352 3.329 3.352 3.328z" fill="#436FCC"/> </g> </svg> </span> </a> </div> <p id="info-comment-conflict-tip" class="text-left">Please list any fees and grants from, employment by, consultancy for, shared ownership in or any close relationship with, at any time over the preceding 36 months, any organisation whose interests may be affected by the publication of the response. 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