{"id":192085,"date":"2015-03-11T00:00:00","date_gmt":"2015-03-11T11:16:41","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/fast-dual-tree-k-means-with-bounded-single-iteration-runtime\/"},"modified":"2016-07-15T15:22:52","modified_gmt":"2016-07-15T22:22:52","slug":"fast-dual-tree-k-means-with-bounded-single-iteration-runtime","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/fast-dual-tree-k-means-with-bounded-single-iteration-runtime\/","title":{"rendered":"Fast Dual-Tree k-means with Bounded Single-Iteration Runtime"},"content":{"rendered":"<div class=\"asset-content\">\n<p>k-means is a widely used clustering algorithm, but for k clusters and a dataset size of N, each iteration of Lloyd&#8217;s algorithm costs O(kN) time.  Although there are a handful of techniques to accelerate single Lloyd iterations, none of these techniques are tailored to the case of large k, which is increasingly common as dataset sizes grow (one example: vector quantization), and none of these techniques have a worst-case runtime bound of less than O(kN) per iteration.  I present a dual-tree algorithm with a worst-case runtime bound of O(N + k log  k) under certain assumptions on the dataset, and show that this algorithm outperforms all other alternatives as k and N grow.  An implementation is readily available in mlpack.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>k-means is a widely used clustering algorithm, but for k clusters and a dataset size of N, each iteration of Lloyd&#8217;s algorithm costs O(kN) time. Although there are a handful of techniques to accelerate single Lloyd iterations, none of these techniques are tailored to the case of large k, which is increasingly common as dataset [&hellip;]<\/p>\n","protected":false},"featured_media":198941,"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-192085","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/5-hdC2mo0zo","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192085","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\/192085\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/198941"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=192085"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=192085"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=192085"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=192085"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=192085"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=192085"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=192085"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=192085"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=192085"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=192085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}