A Kernel Classifier using Linearised Bregman Iteration

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K Wimalawarne"> <meta name="citation_publication_date" content="2009/04/23"> <meta name="citation_journal_title" content="International Journal of Computer and Information Engineering"> <meta name="citation_volume" content="3"> <meta name="citation_issue" content="4"> <meta name="citation_firstpage" content="1166"> <meta name="citation_lastpage" content="1169"> <meta name="citation_pdf_url" content="https://publications.waset.org/8398/pdf"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value=""> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 33122</div> </div> </div> </div> <div class="card publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">A Kernel Classifier using Linearised Bregman Iteration</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/search?q=K.%20A.%20D.%20N.%20K%20Wimalawarne">K. A. D. N. K Wimalawarne</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we introduce a novel kernel classifier based on a iterative shrinkage algorithm developed for compressive sensing. We have adopted Bregman iteration with soft and hard shrinkage functions and generalized hinge loss for solving l1 norm minimization problem for classification. Our experimental results with face recognition and digit classification using SVM as the benchmark have shown that our method has a close error rate compared to SVM but do not perform better than SVM. We have found that the soft shrinkage method give more accuracy and in some situations more sparseness than hard shrinkage methods. <iframe src="https://publications.waset.org/8398.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/search?q=Compressive%20sensing" title="Compressive sensing">Compressive sensing</a>, <a href="https://publications.waset.org/search?q=Bregman%20iteration" title=" Bregman iteration"> Bregman iteration</a>, <a href="https://publications.waset.org/search?q=Generalisedhinge%20loss" title=" Generalisedhinge loss"> Generalisedhinge loss</a>, <a href="https://publications.waset.org/search?q=sparse" title=" sparse"> sparse</a>, <a href="https://publications.waset.org/search?q=kernels" title=" kernels"> kernels</a>, <a href="https://publications.waset.org/search?q=shrinkage%20functions" title=" shrinkage functions"> shrinkage functions</a> </p> <p class="card-text"><strong>Digital Object Identifier (DOI):</strong> <a href="https://doi.org/10.5281/zenodo.1070817" target="_blank">doi.org/10.5281/zenodo.1070817</a> </p> <a href="https://publications.waset.org/8398/a-kernel-classifier-using-linearised-bregman-iteration" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/8398/apa" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">APA</a> <a href="https://publications.waset.org/8398/bibtex" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">BibTeX</a> <a href="https://publications.waset.org/8398/chicago" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Chicago</a> <a href="https://publications.waset.org/8398/endnote" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">EndNote</a> <a href="https://publications.waset.org/8398/harvard" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">Harvard</a> <a href="https://publications.waset.org/8398/json" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">JSON</a> <a href="https://publications.waset.org/8398/mla" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">MLA</a> <a href="https://publications.waset.org/8398/ris" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">RIS</a> <a href="https://publications.waset.org/8398/xml" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">XML</a> <a href="https://publications.waset.org/8398/iso690" target="_blank" rel="nofollow" class="btn btn-primary btn-sm">ISO 690</a> <a href="https://publications.waset.org/8398.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">1380</span> </span> <p class="card-text"><strong>References:</strong></p> <br>[1] Donoho. D.L.: "Compressed sensing", IEEE Trans. Inform. Theory, 52:1289-1306, (2006) <br>[2] Daubechies I., Defrise M., De Mol C. "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint", Comm. Pure Appl. Math. 57, pp. 14131457 (2004) <br>[3] Beck A., Teboulle M.,"A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems", SIAM J. Imaging Sciences, forthcoming. <br>[4] YinW., Osher S., Goldfarb D., Darbon J., "Bregman Iterative Algorithms for l1-Minimization with Applications to Compressed Sensing", SIAM J. IMAGING SCIENCES Vol. 1, No. 1, pp. 143168 (2008) <br>[5] Tibshirani R., "Regression selection and shrinkage via the lasso",J. R. Stat. Soc. Ser. B 58, pp. 267288 (1996) <br>[6] Zhu J., Rosset S., Hastie T., Tibshirani R., "1-norm Support Vector Machines", Advances in Neural Information Processing Systems 16, (2003) <br>[7] Raina R., Battle A., Lee H., Packer B., Ng. A. Y., "Self-taught learning: Transfer learning from unlabeled data", ICML 2007 <br>[8] Lee H., Battle A., Raina R., Ng. A. Y., "Efficient sparse coding algorithms", In Advances in Neural Information Processing Systems 19 (NIPS-06), pages 801808, (2007) <br>[9] Langford J., Li L. Zhang T., "Sparse Online Learning via Truncated Gradient", Journal of Machine Learning Research Vol. 10, pp. 777-801 (2009) <br>[10] Koh K., Kim S., Boyd S., "An Interior-Point Method for Large- Scale l1-Regularized Logistic Regression", Journal of Machine Learning Research Vol. 8, pp. 1519-1555, 2007. <br>[11] Hale E., Yin W., Zhang. Y., "A Fixed-point continuation method for l1-regularization with application to compressed sensing", CAAM Technical Report TR07-07, Rice University, Houston, TX, 2007. <br>[12] Vapnik V. N., Statsitical Leanring Theory, Wiley Interscience, (1998) <br>[13] Rennie J.D.M., "Smooth Hinge Classfication", Technical report, MIT (2005) <br>[14] Bredies K., Lorenz D. A., "Iterated hard shrinkage for minimization problems with sparsity constraints", SIAM Journal on Scientific Computing, Vol. 30(2), pp. 657-683, 2008. <br>[15] Graham D. B., Allinson N. M., "Characterizing Virtual Eigensignatures for General Purpose Face Recognition", in Face Recognition: From Theory to Applications , NATO ASI Series F, Computer and Systems Sciences, Vol. 163. H. Wechsler, P. J. Phillips, V. Bruce, F. Fogelman- Soulie and T. S. Huang (eds), pp 446-456, 1998. <br>[16] Campbell C., Cristianini N., "Simple Learning Algorithms for Traning Support Vector Machines", Technical Report, UNiversity of Bristol, 1998. <br>[17] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. 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A Kernel Classifier using Linearised Bregman Iteration