{"id":160276,"date":"2010-12-14T00:00:00","date_gmt":"2010-12-14T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/learning-a-bi-stochastic-data-similarity-matrix\/"},"modified":"2018-10-16T20:14:37","modified_gmt":"2018-10-17T03:14:37","slug":"learning-a-bi-stochastic-data-similarity-matrix","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/learning-a-bi-stochastic-data-similarity-matrix\/","title":{"rendered":"Learning a Bi-Stochastic Data Similarity Matrix"},"content":{"rendered":"<div class=\"asset-content\">\n<p>An idealized clustering algorithm seeks to learn a cluster-adjacency matrix such that, if two data points belong to the same cluster, the corresponding entry would be 1; otherwise the entry would be 0. This integer (1\/0) constraint makes it difficult to find the optimal solution. We propose a relaxation on the cluster-adjacency matrix, by deriving a bi-stochastic matrix from a data similarity (e.g., kernel) matrix according to the Bregman divergence. Our general method is named the Bregmanian Bi-Stochastication (BBS) algorithm.<\/p>\n<p>We focus on two popular choices of the Bregman divergence: the Euclidian distance and he KL divergence. Interestingly, the BBS algorithm using the KL divergence is equivalent to the Sinkhorn-Knopp (SK) algorithm for deriving bi-stochastic matrices. We show that the BBS algorithm using the Euclidian distance is closely related to the relaxed k-means clustering and can often produce noticeably superior clustering results than the SK algorithm (and other algorithms such as Normalized Cut), through extensive experiments on public data sets.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>An idealized clustering algorithm seeks to learn a cluster-adjacency matrix such that, if two data points belong to the same cluster, the corresponding entry would be 1; otherwise the entry would be 0. This integer (1\/0) constraint makes it difficult to find the optimal solution. We propose a relaxation on the cluster-adjacency matrix, by deriving [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13556,13555],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-160276","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-research-area-search-information-retrieval","msr-locale-en_us"],"msr_publishername":"IEEE","msr_edition":"The 10th International Conference on Data Mining 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Wang","user_id":0,"rest_url":false},{"type":"text","value":"Ping Li","user_id":0,"rest_url":false},{"type":"user_nicename","value":"chrisko","user_id":31427,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=chrisko"},{"type":"text","value":"Arnd Christian K\u00f6nig","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[957177],"msr_project":[169514],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/160276"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/160276\/revisions"}],"predecessor-version":[{"id":525060,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/160276\/revisions\/525060"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=160276"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=160276"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=160276"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=160276"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=160276"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=160276"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=160276"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=160276"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=160276"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=160276"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=160276"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=160276"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=160276"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=160276"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=160276"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}