{"id":481,"date":"2017-08-15T10:36:11","date_gmt":"2017-08-15T10:36:11","guid":{"rendered":"http:\/\/web.eecs.umich.edu\/~girasole\/?page_id=481"},"modified":"2022-08-03T08:41:43","modified_gmt":"2022-08-03T08:41:43","slug":"subspace-clustering","status":"publish","type":"page","link":"https:\/\/web.eecs.umich.edu\/~girasole\/?page_id=481","title":{"rendered":"Subspace Clustering"},"content":{"rendered":"<p>Clustering is one of the most commonly used data exploration tools, but data often hold interesting geometric structure for which generic clustering objectives are too coarse. Subspace clustering is a simple generalization that tries to fit each cluster with a low-dimensional subspace (ie, each cluster has&nbsp;a low-dimensional covariance structure). This is a very useful model for many problems in computer vision and computer network topology inference. Our group has developed state-of-the-art approaches for subspace clustering when the data matrix is incomplete&nbsp;and in the active clustering context.<\/p>\n<p style=\"position: absolute;left: -29143px;\">Hanno scoperto che nei pazienti affetti da ipertrofia ventricolare sinistra (una condizione in cui il muscolo cardiaco si ispessisce), l&#8217;ingrediente del Viagra ha impedito al cuore di ingrandirsi e cambiare forma. Inoltre, il PDE5i ha migliorato la funzione cardiaca <a href=\"https:\/\/hookupapp.vip\/privatedelights-memphis\" target=\"_blank\" rel=\"noopener\">privatedelights<\/a> in tutti i pazienti, indipendentemente dalle loro condizioni mediche, e non ha avuto effetti collaterali sulla pressione sanguigna.<\/p>\n<div id=\"zotpress-8f51bcb906db62820bbe2304e18aa0fc\" class=\"zp-Zotpress zp-Zotpress-Bib wp-block-group\">\n\n\t\t<span class=\"ZP_API_USER_ID ZP_ATTR\">1399621<\/span>\n\t\t<span class=\"ZP_ITEM_KEY ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_COLLECTION_ID ZP_ATTR\">6JKB3X7P<\/span>\n\t\t<span class=\"ZP_TAG_ID ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_AUTHOR ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_YEAR ZP_ATTR\"><\/span>\n        <span class=\"ZP_ITEMTYPE ZP_ATTR\"><\/span>\n\t\t<span class=\"ZP_INCLUSIVE ZP_ATTR\">1<\/span>\n\t\t<span class=\"ZP_STYLE ZP_ATTR\">apa<\/span>\n\t\t<span class=\"ZP_LIMIT ZP_ATTR\">50<\/span>\n\t\t<span class=\"ZP_SORTBY ZP_ATTR\">date<\/span>\n\t\t<span 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Low algebraic dimension matrix completion. <i>2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)<\/i>, 790\u2013797. <a class='zp-DOIURL' href='https:\/\/doi.org\/10.1109\/ALLERTON.2017.8262820'>https:\/\/doi.org\/10.1109\/ALLERTON.2017.8262820<\/a><\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-481-1399621-KP7GFVDR\" data-zp-author-date='Pimentel-Alarc\u00f3n-et-al.-2017-07' data-zp-date-author='2017-07-Pimentel-Alarc\u00f3n-et-al.' data-zp-date='2017-07' data-zp-year='2017' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 2; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Pimentel-Alarc\u00f3n, D., Balzano, L., Marcia, R., Nowak, R., & Willett, R. (2017). Mixture regression as subspace clustering. <i>2017 International Conference on Sampling Theory and Applications (SampTA)<\/i>, 456\u2013459. <a class='zp-DOIURL' href='https:\/\/doi.org\/10.1109\/SAMPTA.2017.8024386'>https:\/\/doi.org\/10.1109\/SAMPTA.2017.8024386<\/a><\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-481-1399621-5KU92TTX\" data-zp-author-date='Pimentel-Alarc\u00f3n-et-al.-2016-06' data-zp-date-author='2016-06-Pimentel-Alarc\u00f3n-et-al.' data-zp-date='2016-06' data-zp-year='2016' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 2; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Pimentel-Alarc\u00f3n, D., Balzano, L., Marcia, R., Nowak, R., & Willett, R. (2016). Group-sparse subspace clustering with missing data. <i>2016 IEEE Statistical Signal Processing Workshop (SSP)<\/i>, 1\u20135. <a class='zp-DOIURL' href='https:\/\/doi.org\/10.1109\/SSP.2016.7551734'>https:\/\/doi.org\/10.1109\/SSP.2016.7551734<\/a><\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-481-1399621-BHWNWAUV\" data-zp-author-date='Pimentel-Alarc\u00f3n-et-al.-2016' data-zp-date-author='2016-Pimentel-Alarc\u00f3n-et-al.' data-zp-date='2016' data-zp-year='2016' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 2; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Pimentel-Alarc\u00f3n, D., Balzano, L., & Nowak, R. (2016). Necessary and sufficient conditions for sketched subspace clustering. <i>Allerton Conference on Communication, Control, and Computing<\/i>. <a class='zp-ItemURL' href='https:\/\/danielpimentel.github.io\/pdfs\/sketchedSC.pdf'>https:\/\/danielpimentel.github.io\/pdfs\/sketchedSC.pdf<\/a><\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-481-1399621-78Q9AHXX\" data-zp-author-date='Lipor-and-Balzano-2015-12' data-zp-date-author='2015-12-Lipor-and-Balzano' data-zp-date='2015-12' data-zp-year='2015' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 2; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Lipor, J., & Balzano, L. (2015). 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On the sample complexity of subspace clustering with missing data. <i>2014 IEEE Workshop on Statistical Signal Processing (SSP)<\/i>, 280\u2013283. <a class='zp-ItemURL' href='http:\/\/ieeexplore.ieee.org\/xpl\/articleDetails.jsp?arnumber=6884630'>http:\/\/ieeexplore.ieee.org\/xpl\/articleDetails.jsp?arnumber=6884630<\/a><\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-481-1399621-GTXPRIVJ\" data-zp-author-date='Eriksson-et-al.-2012' data-zp-date-author='2012-Eriksson-et-al.' data-zp-date='2012' data-zp-year='2012' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 2; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Eriksson, B., Balzano, L., & Nowak, R. (2012). High rank matrix completion. <i>Proc. of Intl. Conf. on Artificial Intell. and Stat<\/i>. <a class='zp-ItemURL' href='http:\/\/jmlr.csail.mit.edu\/proceedings\/papers\/v22\/eriksson12\/eriksson12.pdf'>http:\/\/jmlr.csail.mit.edu\/proceedings\/papers\/v22\/eriksson12\/eriksson12.pdf<\/a> <sup class=\"zp-Notes-Reference\"><a href=\"#zp-Note-GTXPRIVJ\">1<\/a><\/sup> <\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\t\t\t\t<div id=\"zp-ID-481-1399621-ZPS2BSDF\" data-zp-author-date='Balzano-et-al.-2012' data-zp-date-author='2012-Balzano-et-al.' data-zp-date='2012' data-zp-year='2012' data-zp-itemtype='conferencePaper' class=\"zp-Entry zpSearchResultsItem\">\n<div class=\"csl-bib-body\" style=\"line-height: 2; padding-left: 1em; text-indent:-1em;\">\n  <div class=\"csl-entry\">Balzano, L., Szlam, A., Recht, B., & Nowak, R. (2012). K-subspaces with missing data. <i>Statistical Signal Processing Workshop (SSP), 2012 IEEE<\/i>, 612\u2013615. <a class='zp-ItemURL' href='http:\/\/ieeexplore.ieee.org\/xpls\/abs_all.jsp?arnumber=6319774'>http:\/\/ieeexplore.ieee.org\/xpls\/abs_all.jsp?arnumber=6319774<\/a><\/div>\n<\/div>\n\t\t\t\t<\/div><!-- .zp-Entry .zpSearchResultsItem -->\n\t\t\t<\/div><!-- .zp-zp-SEO-Content -->\n\t\t<\/div><!-- .zp-List -->\n\t<\/div><!--.zp-Zotpress-->\n\n\n","protected":false},"excerpt":{"rendered":"<p>Clustering is one of the most commonly used data exploration tools, but data often hold interesting geometric structure for which generic clustering objectives are too coarse. Subspace clustering is a simple generalization that tries to fit each cluster with a low-dimensional subspace (ie, each cluster has&nbsp;a low-dimensional covariance structure). This is a very useful model [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":182,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/481"}],"collection":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/types\/page"}],"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=481"}],"version-history":[{"count":4,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/481\/revisions"}],"predecessor-version":[{"id":858,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/481\/revisions\/858"}],"up":[{"embeddable":true,"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=\/wp\/v2\/pages\/182"}],"wp:attachment":[{"href":"https:\/\/web.eecs.umich.edu\/~girasole\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}