{"id":149956,"date":"1997-01-01T00:00:00","date_gmt":"1997-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/gtm-a-principled-alternative-to-the-self-organizing-map\/"},"modified":"2018-10-16T21:50:03","modified_gmt":"2018-10-17T04:50:03","slug":"gtm-a-principled-alternative-to-the-self-organizing-map","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/gtm-a-principled-alternative-to-the-self-organizing-map\/","title":{"rendered":"GTM: a principled alternative to the Self-Organizing Map"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. We introduce a novel form of latent variable model, which we call the GTM algorithm (for Generative Topographic Mapping), which allows general non-linear transformations from latent space to data space, and which is trained using the EM (expectation-maximization) algorithm. Our approach overcomes the limitations of the SOM, while introducing no significant disadvantages. We demonstrate the performance of the GTM algorithm on simulated data from flow diagnostics for a multi-phase oil pipeline.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Self-Organizing Map (SOM) algorithm has been extensively studied and has been applied with considerable success to a wide variety of problems. However, the algorithm is derived from heuristic ideas and this leads to a number of significant limitations. In this paper, we consider the problem of modelling the probability density of data in a [&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":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-149956","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"Springer","msr_edition":"International Conference on Artificial Neural Networks, ICANN'96","msr_affiliation":"","msr_published_date":"1997-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"165\u2013170","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"9","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","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":"211545","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"bishop-gtm-nips-97.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/bishop-gtm-nips-97.pdf","id":211545,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":211545,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/bishop-gtm-nips-97.pdf"}],"msr-author-ordering":[{"type":"user_nicename","value":"cmbishop","user_id":31452,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=cmbishop"},{"type":"user_nicename","value":"markussv","user_id":32820,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=markussv"},{"type":"text","value":"Christopher K. 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