{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T10:59:34Z","timestamp":1760266774009},"reference-count":39,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2007,2]]},"abstract":"<jats:p> Linear discrimination, from the point of view of numerical linear algebra, can be treated as solving an ill-posed system of linear equations. In order to generate a solution that is robust in the presence of noise, these problems require regularization. Here, we examine the ill-posedness involved in the linear discrimination of cancer gene expression data with respect to outcome and tumor subclasses. We show that a filter factor representation, based upon Singular Value Decomposition, yields insight into the numerical ill-posedness of the hyperplane-based separation when applied to gene expression data. We also show that this representation yields useful diagnostic tools for guiding the selection of classifier parameters, thus leading to improved performance. <\/jats:p>","DOI":"10.1142\/s0219720007002539","type":"journal-article","created":{"date-parts":[[2007,4,30]],"date-time":"2007-04-30T11:37:04Z","timestamp":1177933024000},"page":"79-104","source":"Crossref","is-referenced-by-count":4,"title":["REGULARIZATION STRATEGIES FOR HYPERPLANE CLASSIFIERS: APPLICATION TO CANCER CLASSIFICATION WITH GENE EXPRESSION DATA"],"prefix":"10.1142","volume":"05","author":[{"given":"ERIK","family":"ANDRIES","sequence":"first","affiliation":[{"name":"Departments of Mathematics &amp; Statistics and, Center for High Performance Computing, University of New Mexico, Albuquerque, NM 87131, USA"}]},{"given":"THOMAS","family":"HAGSTROM","sequence":"additional","affiliation":[{"name":"Department of Mathematics &amp; Statistics, University of New Mexico, Albuquerque, NM 87131, USA"}]},{"given":"SUSAN R.","family":"ATLAS","sequence":"additional","affiliation":[{"name":"Center for Advanced Studies and Department of Physics &amp; Astronomy, University of New Mexico, Albuquerque, NM 87131, USA"}]},{"given":"CHERYL","family":"WILLMAN","sequence":"additional","affiliation":[{"name":"Cancer Research and Treatment Center and Department of Pathology, University of New Mexico, Albuquerque, NM 87131, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/85.1.115"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.97.18.10101"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.102102699"},{"key":"rf6","volume-title":"Parameter Estimation and Inverse Problems","author":"Aster R.","year":"2004"},{"key":"rf8","volume-title":"Nonlinear Programming","author":"Bertsekas D.","year":"1999"},{"key":"rf9","first-page":"102","author":"Carroll W. 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