spectral clustering and embedding with hidden markov models

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1、SpectralClusteringandEmbeddingwithHiddenMarkovModelsTonyJebara,YingboSong,andKapilThadanifjebara,yingbo,kapilg@cs.columbia.eduDepartmentofComputerScience,ColumbiaUniversity,NewYorkNY10027,USAAbstract.Clusteringhasrecentlyenjoyedprogressviaspectralmeth-od

2、swhichgroupdatausingonlypairwiseanitiesandavoidparametricassumptions.Whilespectralclusteringofvectorinputsisstraightfor-ward,extensionstostructureddataortime-seriesdataremainlessex-plored.Thispaperproposesaclusteringmethodfortime-seriesdatathatcouplesno

3、n-parametricspectralclusteringwithparametrichiddenMarkovmodels(HMMs).HMMsaddsomebenecialstructuralandparametricassumptionssuchasMarkovpropertiesandhiddenstatevariableswhichareusefulforclustering.Thisarticleshowsthatus-ingprobabilisticpairwisekernelestim

4、atesbetweenparametricmodelsprovidesimprovedexperimentalresultsforunsupervisedclusteringandvisualizationofrealandsyntheticdatasets.Resultsarecomparedwithafullyparametricbaselinemethod(amixtureofhiddenMarkovmodels)andanon-parametricbaselinemethod(spectralc

5、lusteringwithnon-parametrictime-serieskernels).1IntroductionThispaperexploresunsupervisedlearninginthetime-seriesdomainusingacom-binationofparametricandnon-parametricmethods.Someparametricassump-tions,suchasMarkovassumptionsandhiddenstateassumptions,areq

6、uiteusefulfortime-seriesdata.However,itisalsoadvantageoustoremainnon-parametricandagnosticabouttheoverallshapethatacollectionoftime-seriesdataforms.Thispaperprovidessurprisingempiricalevidencethatasemi-parametric[1,2]methodcanoutperformbothfullyparametri

7、cmethodsofdescribingmultipletime-seriesobservationsandfullynon-parametricmethods.Theseimprovementsincludebetterclusteringperformanceaswellasbetterembeddingandvisual-izationoverexistingstate-of-the-arttime-seriestechniques.Thereareavarietyofparametricandn

8、on-parametricalgorithmsfordiscov-eringclusterswithinadataset;however,theapplicationofthesetechniquesforclusteringsequentialdatasuchastime-seriesdataposesanumberofadditionalchallenges.Time-seriesdatahasinherentstructurewhic