{"id":575,"date":"2018-09-16T13:14:43","date_gmt":"2018-09-16T13:14:43","guid":{"rendered":"http:\/\/web.eecs.umich.edu\/~girasole\/?p=575"},"modified":"2026-07-23T02:07:04","modified_gmt":"2026-07-23T02:07:04","slug":"improving-k-subspaces-via-coherence-pursuit","status":"publish","type":"post","link":"https:\/\/web.eecs.umich.edu\/~girasole\/?p=575","title":{"rendered":"Improving K-Subspaces via Coherence Pursuit"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">John Lipor, Andrew Gitlin, Bioashuai Tao, and I have a new paper, &#8220;<a href=\"https:\/\/ieeexplore.ieee.org\/document\/8457298\/\">Improving K-Subspaces via Coherence Pursuit<\/a>,&#8221; to be published in the Journal of Special Topics in Signal Processing issue &#8220;Robust Subspace Learning and Tracking: Theory, Algorithms, and Applications.&#8221; In it we present a new subspace clustering algorithm, Coherence Pursuit &#8211; K-Subspaces (CoP-KSS). Here is the <a href=\"http:\/\/web.cecs.pdx.edu\/~lipor\/Code\/gitlin2018improving.zip\">code for CoP-KSS<\/a> and for our figures. Our paper considers specifically the PCA step in K-Subspaces, where a best-fit subspace estimate is determined from a (possibly incorrect) clustering. When a given cluster has points from multiple low-rank subspaces, PCA is not a robust approach. We replace that step with Coherence Pursuit, a new algorithm for Robust PCA. We prove that Coherence Pursuit indeed can recover the &#8220;majority&#8221; subspace when data from other low-rank subspaces is contaminating the cluster. In this paper we also prove &#8212; to the best of our knowledge, for the first time &#8212; that the K-Subspaces problem is NP-hard, and indeed even NP-hard to approximate within any finite factor for large enough subspace rank.\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>John Lipor, Andrew Gitlin, Bioashuai Tao, and I have a new paper, &#8220;Improving K-Subspaces via Coherence Pursuit,&#8221; to be published in the Journal of Special Topics in Signal Processing issue &#8220;Robust Subspace Learning and Tracking: Theory, Algorithms, and Applications.&#8221; In it we present a new subspace clustering algorithm, Coherence Pursuit &#8211; K-Subspaces (CoP-KSS). Here is [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4,13],"tags":[],"class_list":["post-575","post","type-post","status-publish","format-standard","hentry","category-code","category-news","category-spada","entry"],"_links":{"self":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts\/575","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=575"}],"version-history":[{"count":4,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts\/575\/revisions"}],"predecessor-version":[{"id":1088,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/posts\/575\/revisions\/1088"}],"wp:attachment":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}