{"id":149955,"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-through-time\/"},"modified":"2018-10-16T21:49:49","modified_gmt":"2018-10-17T04:49:49","slug":"gtm-through-time","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/gtm-through-time\/","title":{"rendered":"GTM through time"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (i.i.d.) vectors. For time series, however, the i.i.d. assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the emission density in a hidden Markov model. Since GTM has discrete hidden states we are able to find a tractable EM algorithm, based on the forward-backward algorithm, to train the model. We illustrate the performance of GTM through time using flight recorder data from a helicopter.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The standard GTM (generative topographic mapping) algorithm assumes that the data on which it is trained consists of independent, identically distributed (i.i.d.) vectors. For time series, however, the i.i.d. assumption is a poor approximation. In this paper we show how the GTM algorithm can be extended to model time series by incorporating it as the [&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-149955","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Proceedings IEE Fifth International Conference on Artificial Neural Networks, Cambridge, U.K.","msr_affiliation":"","msr_published_date":"1997-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"111\u2013116","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","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":"211538","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"bishop-gtmtt-iee-97.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/bishop-gtmtt-iee-97.pdf","id":211538,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":211538,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/bishop-gtmtt-iee-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":"text","value":"Geoffrey E. 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