Learning the parts of objects by non-negative matrix factorization

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There is psychological1 and physiological2,3 evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations4,5. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic strengths do not change sign.","datePublished":"","dateModified":"","pageStart":"788","pageEnd":"791","sameAs":"https://doi.org/10.1038/44565","keywords":["Science","Humanities and Social Sciences","multidisciplinary"],"image":["https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2F44565/MediaObjects/41586_1999_Article_BF44565_Fig1_HTML.gif","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2F44565/MediaObjects/41586_1999_Article_BF44565_Fig2_HTML.gif","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2F44565/MediaObjects/41586_1999_Article_BF44565_Fig3_HTML.gif","https://media.springernature.com/lw1200/springer-static/image/art%3A10.1038%2F44565/MediaObjects/41586_1999_Article_BF44565_Fig4_HTML.gif"],"isPartOf":{"name":"Nature","issn":["1476-4687","0028-0836"],"volumeNumber":"401","@type":["Periodical","PublicationVolume"]},"publisher":{"name":"Nature Publishing Group UK","logo":{"url":"https://www.springernature.com/app-sn/public/images/logo-springernature.png","@type":"ImageObject"},"@type":"Organization"},"author":[{"name":"Daniel D. 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Sebastian Seung","affiliation":[{"name":"Bell Laboratories, Lucent Technologies ","address":{"name":"Bell Laboratories, Lucent Technologies , Murray Hill, USA","@type":"PostalAddress"},"@type":"Organization"},{"name":"Massachusetts Institute of Technology","address":{"name":"Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, USA","@type":"PostalAddress"},"@type":"Organization"}],"@type":"Person"}],"isAccessibleForFree":false,"hasPart":{"isAccessibleForFree":false,"cssSelector":".main-content","@type":"WebPageElement"},"@type":"ScholarlyArticle"},"@context":"https://schema.org","@type":"WebPage"}</script> <link rel="canonical" href="https://www.nature.com/articles/44565"> <meta name="journal_id" content="41586"/> <meta name="dc.title" content="Learning the parts of objects by non-negative matrix factorization"/> <meta name="dc.source" content="Nature 1999 401:6755"/> <meta name="dc.format" content="text/html"/> <meta name="dc.publisher" content="Nature Publishing Group"/> <meta name="dc.type" content="OriginalPaper"/> <meta name="dc.language" content="En"/> <meta name="dc.copyright" content="1999 Macmillan Magazines Ltd."/> <meta name="dc.rights" content="1999 Macmillan Magazines Ltd."/> <meta name="dc.rightsAgent" content="journalpermissions@springernature.com"/> <meta name="dc.description" content="Is perception of the whole based on perception of its parts? There is psychological1 and physiological2,3 evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations4,5. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. 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There is psychological1 and physiological2,3 evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations4,5. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. 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class="c-article-header"> <header> <ul class="c-article-identifiers" data-test="article-identifier"> <li class="c-article-identifiers__item" data-test="article-category">Letter</li> <li class="c-article-identifiers__item">Published: <time datetime="1999-10-21">21 October 1999</time></li> </ul> <h1 class="c-article-title" data-test="article-title" data-article-title="">Learning the parts of objects by non-negative matrix factorization</h1> <ul class="c-article-author-list c-article-author-list--short" data-test="authors-list" data-component-authors-activator="authors-list"><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-Daniel_D_-Lee-Aff1" data-author-popup="auth-Daniel_D_-Lee-Aff1" data-author-search="Lee, Daniel D.">Daniel D. Lee</a><sup class="u-js-hide"><a href="#Aff1">1</a></sup> & </li><li class="c-article-author-list__item"><a data-test="author-name" data-track="click" data-track-action="open author" data-track-label="link" href="#auth-H__Sebastian-Seung-Aff1-Aff2" data-author-popup="auth-H__Sebastian-Seung-Aff1-Aff2" data-author-search="Seung, H. Sebastian">H. Sebastian Seung</a><sup class="u-js-hide"><a href="#Aff1">1</a>,<a href="#Aff2">2</a></sup> </li></ul> <p class="c-article-info-details" data-container-section="info"> <a data-test="journal-link" href="/" data-track="click" data-track-action="journal homepage" data-track-category="article body" data-track-label="link"><i data-test="journal-title">Nature</i></a> <b data-test="journal-volume"><span class="u-visually-hidden">volume</span> 401</b>, <span class="u-visually-hidden">pages </span>788–791 (<span data-test="article-publication-year">1999</span>)<a href="#citeas" class="c-article-info-details__cite-as u-hide-print" data-track="click" data-track-action="cite this article" data-track-label="link">Cite this article</a> </p> <div class="c-article-metrics-bar__wrapper u-clear-both"> <ul class="c-article-metrics-bar u-list-reset"> <li class=" c-article-metrics-bar__item" data-test="access-count"> <p class="c-article-metrics-bar__count">77k <span class="c-article-metrics-bar__label">Accesses</span></p> </li> <li class="c-article-metrics-bar__item" data-test="citation-count"> <p class="c-article-metrics-bar__count">9020 <span class="c-article-metrics-bar__label">Citations</span></p> </li> <li class="c-article-metrics-bar__item" data-test="altmetric-score"> <p class="c-article-metrics-bar__count">62 <span class="c-article-metrics-bar__label">Altmetric</span></p> </li> <li class="c-article-metrics-bar__item"> <p class="c-article-metrics-bar__details"><a href="/articles/44565/metrics" data-track="click" data-track-action="view metrics" data-track-label="link" rel="nofollow">Metrics <span class="u-visually-hidden">details</span></a></p> </li> </ul> </div> </header> </div> <div class="c-article-body"> <section aria-labelledby="Abs1" data-title="Abstract" lang="en"><div class="c-article-section" id="Abs1-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="Abs1">Abstract</h2><div class="c-article-section__content" id="Abs1-content"><p>Is perception of the whole based on perception of its parts? There is psychological<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 1" title="Palmer,S. E. Hierarchical structure in perceptual representation. Cogn. Psychol. 9, 441–474 ( 1977)." href="/articles/44565#ref-CR1" id="ref-link-section-d13613279e310">1</a></sup> and physiological<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 2" title="Wachsmuth,E., Oram,M. W. & Perrett, D. I. Recognition of objects and their component parts: responses of single units in the temporal cortex of the macaque. Cereb. Cortex 4, 509–522 (1994)." href="/articles/44565#ref-CR2" id="ref-link-section-d13613279e314">2</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 3" title="Logothetis,N. K. & Sheinberg,D. L. Visual object recognition. Annu. Rev. Neurosci. 19, 577 –621 (1996)." href="/articles/44565#ref-CR3" id="ref-link-section-d13613279e317">3</a></sup> evidence for parts-based representations in the brain, and certain computational theories of object recognition rely on such representations<sup><a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 4" title="Biederman,I. Recognition-by-components: a theory of human image understanding. Psychol. Rev. 94, 115–147 (1987)." href="/articles/44565#ref-CR4" id="ref-link-section-d13613279e321">4</a>,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 5" title="Ullman,S. High-Level Vision: Object Recognition and Visual Cognition (MIT Press, Cambridge, MA, 1996)." href="/articles/44565#ref-CR5" id="ref-link-section-d13613279e324">5</a></sup>. But little is known about how brains or computers might learn the parts of objects. Here we demonstrate an algorithm for non-negative matrix factorization that is able to learn parts of faces and semantic features of text. This is in contrast to other methods, such as principal components analysis and vector quantization, that learn holistic, not parts-based, representations. Non-negative matrix factorization is distinguished from the other methods by its use of non-negativity constraints. These constraints lead to a parts-based representation because they allow only additive, not subtractive, combinations. When non-negative matrix factorization is implemented as a neural network, parts-based representations emerge by virtue of two properties: the firing rates of neurons are never negative and synaptic strengths do not change sign.</p></div></div></section> <noscript> <div class="c-nature-box c-nature-box--side " data-component="entitlement-box"> <div class="js-access-button"> <a href="https://wayf.springernature.com?redirect_uri=https%3A%2F%2Fwww.nature.com%2Farticles%2F44565" class="c-article__button" data-test="ra21"> <svg class="u-icon" width="18" height="18" aria-hidden="true" focusable="false"><use href="#icon-institution"></use></svg> <span class="c-article__button-text">Access through your institution</span> </a> </div> <div class="js-buy-button"> <a href="#access-options" class="c-article__button c-article__button--inverted" data-test="ra21"> <span>Buy or subscribe</span> </a> </div> </div> </noscript> <div class="js-context-bar-sticky-point-mobile" data-track-context="article 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C. Papageorgiou and T. Poggio provided us with the database of faces, and R. Sproat with the Grolier encyclopedia corpus. We thank L. Saul for convincing us of the advantages of EM-type algorithms. We have benefited from discussions with B. Anderson, K. Clarkson, R. Freund, L. Kaufman, E. Rietman, S. Roweis, N. Rubin, J. Tenenbaum, N. Tishby, M. Tsodyks, T. Tyson and M. Wright.</p></div></div></section><section aria-labelledby="author-information" data-title="Author information"><div class="c-article-section" id="author-information-section"><h2 class="c-article-section__title js-section-title js-c-reading-companion-sections-item" id="author-information">Author information</h2><div class="c-article-section__content" id="author-information-content"><h3 class="c-article__sub-heading" id="affiliations">Authors and Affiliations</h3><ol class="c-article-author-affiliation__list"><li id="Aff1"><p class="c-article-author-affiliation__address">Bell Laboratories, Lucent Technologies , Murray Hill, 07974, New Jersey, USA</p><p class="c-article-author-affiliation__authors-list">Daniel D. Lee & H. Sebastian Seung</p></li><li id="Aff2"><p class="c-article-author-affiliation__address">Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, 02139, Massachusetts, USA</p><p class="c-article-author-affiliation__authors-list">H. 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Learning the parts of objects by non-negative matrix factorization. <i>Nature</i> <b>401</b>, 788–791 (1999). https://doi.org/10.1038/44565</p><p class="c-bibliographic-information__download-citation u-hide-print"><a data-test="citation-link" data-track="click" data-track-action="download article citation" data-track-label="link" data-track-external="" rel="nofollow" href="https://citation-needed.springer.com/v2/references/10.1038/44565?format=refman&flavour=citation">Download citation<svg width="16" height="16" focusable="false" role="img" aria-hidden="true" class="u-icon"><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#icon-eds-i-download-medium"></use></svg></a></p><ul class="c-bibliographic-information__list" data-test="publication-history"><li class="c-bibliographic-information__list-item"><p>Received<span class="u-hide">: </span><span class="c-bibliographic-information__value"><time datetime="1999-05-24">24 May 1999</time></span></p></li><li 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Learning the parts of objects by non-negative matrix factorization | Nature