{"id":4718,"date":"2025-06-19T07:02:31","date_gmt":"2025-06-19T07:02:31","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/06\/19\/2506-14952\/"},"modified":"2025-06-19T07:02:31","modified_gmt":"2025-06-19T07:02:31","slug":"2506-14952","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/06\/19\/2506-14952\/","title":{"rendered":"An Observation on Lloyd&#8217;s k-Means Algorithm in High Dimensions"},"content":{"rendered":"\n<div>An Observation on Lloyd&#8217;s k-Means Algorithm in High Dimensions<\/div>\n<p> \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2506.14952v1 Announce Type: new<br \/>\nAbstract: Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the failure of k-means in high-dimensional settings with high noise and limited sample sizes, using a simple Gaussian Mixture Model (GMM). We identify regimes where, with high probability, almost every partition of the data becomes a fixed point of the k-means algorithm. This study is motivated by challenges in the analysis of more complex cases, such as masked GMMs, and those arising from applications in Cryo-Electron Microscopy.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    David Silva-S&#8217;anchez, Roy R. Lederman<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2506.14952\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>An Observation on Lloyd&#8217;s k-Means Algorithm in High Dimensions arXiv:2506.14952v1 Announce Type: new Abstract: Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the failure of k-means in high-dimensional settings with [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[778,332,3010],"class_list":["post-4718","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-algorithm","tag-high","tag-means"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4718"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=4718"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4718\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=4718"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=4718"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=4718"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}