{"id":186081,"date":"2011-03-24T00:00:00","date_gmt":"2011-03-28T19:12:47","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/large-matrices-beyond-singular-value-decomposition\/"},"modified":"2016-08-22T11:30:48","modified_gmt":"2016-08-22T18:30:48","slug":"large-matrices-beyond-singular-value-decomposition","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/large-matrices-beyond-singular-value-decomposition\/","title":{"rendered":"Large matrices beyond singular value decomposition"},"content":{"rendered":"<div class=\"asset-content\">\n<p>A number of data sets are naturally described in matrix form. Examples range from microarrays to collaborative filtering data, to the set of pairwise distances of a cloud of points.  In many of these examples, singular value decomposition (SVD) provides an efficient way to construct a low-rank approximation thus achievieng both dimensionality reduction, and effective denoising. SVD is also an important tool in the design of approximate linear algebra algorithms for massive data sets.<\/p>\n<p>It is a recent discovery that &#8211;for important classes of matrices&#8211;SVD is sub-optimal, and can be significantly improved upon. There has been considerable progress on this topic over the last           two years, partly spurred by interest in the Netflix challenge. I will overview this progress, and describe recent results on several specific problems, as well as outstanting challenges.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A number of data sets are naturally described in matrix form. Examples range from microarrays to collaborative filtering data, to the set of pairwise distances of a cloud of points. In many of these examples, singular value decomposition (SVD) provides an efficient way to construct a low-rank approximation thus achievieng both dimensionality reduction, and effective [&hellip;]<\/p>\n","protected":false},"featured_media":196061,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-186081","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/eFWzg_YsXqk","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/186081","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/186081\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/196061"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=186081"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=186081"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=186081"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=186081"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=186081"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=186081"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=186081"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=186081"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=186081"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=186081"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}