{"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":"","msr-author-ordering":null,"msr_publishername":"Springer","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"International Conference on Artificial Neural Networks, ICANN'96","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"165\u2013170","msr_page_range_start":"165","msr_page_range_end":"170","msr_series":"","msr_volume":"9","msr_copyright":"","msr_conference_name":"International Conference on Artificial Neural Networks, ICANN'96","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"M. Svens\u00e9n, C. 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