{"id":421848,"date":"2017-08-25T09:18:09","date_gmt":"2017-08-25T16:18:09","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=421848"},"modified":"2018-10-16T20:17:49","modified_gmt":"2018-10-17T03:17:49","slug":"enhancing-bilinear-subspace-learning-element-rearrangement","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/enhancing-bilinear-subspace-learning-element-rearrangement\/","title":{"rendered":"Enhancing Bilinear Subspace Learning by Element Rearrangement"},"content":{"rendered":"<div id=\"LayoutWrapper\">\n<div class=\"ng-scope\">\n<div>\n<div class=\"pure-g document stats-document ng-isolate-scope\">\n<section class=\"tab-pane pure-u-1-1 u-printing-display-inline-ie u-printing-display-inline-ff\">\n<div class=\"ng-scope\">\n<div class=\"ng-scope\">\n<section id=\"4796206\" class=\"pure-u-1-1 document-abstract document-tab u-p-2 ng-isolate-scope\">\n<div class=\"pure-g\">\n<div class=\"ng-scope pure-u-1-1\">\n<div class=\"ng-scope\">\n<div class=\"abstract-text ng-binding\">The success of bilinear subspace learning heavily depends on reducing correlations among features along rows and columns of the data matrices. In this work, we study the problem of rearranging elements within a matrix in order to maximize these correlations so that information redundancy in matrix data can be more extensively removed by existing bilinear subspace learning algorithms. An efficient iterative algorithm is proposed to tackle this essentially integer programming problem. In each step, the matrix structure is refined with a constrained earth mover&#8217;s distance procedure that incrementally rearranges matrices to become more similar to their low-rank approximations, which have high correlation among features along rows and columns. In addition, we present two extensions of the algorithm for conducting supervised bilinear subspace learning. Experiments in both unsupervised and supervised bilinear subspace learning demonstrate the effectiveness of our proposed algorithms in improving data compression performance and classification accuracy.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The success of bilinear subspace learning heavily depends on reducing correlations among features along rows and columns of the data matrices. In this work, we study the problem of rearranging elements within a matrix in order to maximize these correlations so that information redundancy in matrix data can be more extensively removed by existing bilinear [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"10","msr_journal":"IEEE Transactions on Pattern Analysis and Machine Intelligence","msr_number":"","msr_organization":"","msr_pages_string":"1913-1920","msr_page_range_start":"1913","msr_page_range_end":"1920","msr_series":"","msr_volume":"31","msr_copyright":"","msr_conference_name":"","msr_doi":"10.1109\/TPAMI.2009.51","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2009-02-27","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"http:\/\/ieeexplore.ieee.org\/abstract\/document\/4796206\/","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13562],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-421848","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-computer-vision","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2009-02-27","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"1913-1920","msr_chapter":"","msr_isbn":"","msr_journal":"IEEE Transactions on Pattern Analysis and Machine Intelligence","msr_volume":"31","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"10","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"","msr_publicationurl":"http:\/\/ieeexplore.ieee.org\/abstract\/document\/4796206\/","msr_doi":"10.1109\/TPAMI.2009.51","msr_publication_uploader":[{"type":"url","title":"http:\/\/ieeexplore.ieee.org\/abstract\/document\/4796206\/","viewUrl":false,"id":false,"label_id":0},{"type":"doi","title":"10.1109\/TPAMI.2009.51","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":0,"url":"http:\/\/ieeexplore.ieee.org\/abstract\/document\/4796206\/"}],"msr-author-ordering":[{"type":"text","value":"Dong Xu","user_id":0,"rest_url":false},{"type":"text","value":"Shuicheng Yan","user_id":0,"rest_url":false},{"type":"edited_text","value":"Stephen Lin","user_id":33735,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Stephen Lin"},{"type":"text","value":"Thomas S. 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