{"id":188237,"date":"2012-08-02T00:00:00","date_gmt":"2012-08-14T11:05:38","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/clustering\/"},"modified":"2016-08-22T11:26:46","modified_gmt":"2016-08-22T18:26:46","slug":"clustering","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/clustering\/","title":{"rendered":"Clustering"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Clustering is the problem of finding a &#8220;good&#8221;\u0092\u0092 partition of a set of data points in d space into clusters (groups, each consisting of &#8220;nearby&#8221;\u0092\u0092 points). In the worst-case, the problem is hard. This can be overcome in two ways: Assuming stochastic models of data, the &#8220;correct\u0092\u0092&#8221; clustering can be found. The last decade has seen many detailed results in this setting. A second alternative is to make no stochastic assumptions, but settle for non-optimal solutions. The workhorse of this approach is Lloyd\u0092s k-means algorithm.  After surveying both alternatives, I will describe a recent result (joint work with Amit Kumar) which, qualitatively, seems to provide the best of both worlds.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Clustering is the problem of finding a &#8220;good&#8221;\u0092\u0092 partition of a set of data points in d space into clusters (groups, each consisting of &#8220;nearby&#8221;\u0092\u0092 points). In the worst-case, the problem is hard. This can be overcome in two ways: Assuming stochastic models of data, the &#8220;correct\u0092\u0092&#8221; clustering can be found. The last decade has [&hellip;]<\/p>\n","protected":false},"featured_media":197073,"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-188237","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/ZROrDZBPOrI","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/188237","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\/188237\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197073"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=188237"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=188237"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=188237"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=188237"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=188237"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=188237"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=188237"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=188237"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=188237"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=188237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}