1644-generalized-model-selection-for-unsupervised-learning-in-high-dimensions无监督的广义模型选择 高维度学习

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1、GeneralizedModelSelectionForUnsupervisedLearningInHighDimensionsShivakumarVaithyanathanByronDomIBMAlmadenResearchCenterIBMAlmadenResearchCenter650HarryRoad650HarryRoadSanJose,CA95136SanJose,CA95136Shiv@almaden.ibm.comdom@almaden.ibm.comAbstractWedescribeaBaye

2、sianapproachtomodelselectioninunsupervisedlearningthatdeterminesboththefeaturesetandthenumberofclusters.Wethenevaluatethisscheme(basedonmarginallikelihood)andonebasedoncross-validatedlikelihood.FortheBayesianschemewederiveaclosed-formsolutionofthemarginallike

3、lihoodbyassumingappropriateformsofthelikelihoodfunctionandprior.Extensiveexperimentscomparetheseapproachesandallresultsareverifiedbycomparisonagainstgroundtruth.IntheseexperimentstheBayesianschemeusingourobjectivefunctiongavebetterresultsthancross-validation.

4、1IntroductionRecenteffortsdefinethemodelselectionproblemasoneofestimatingthenumberofclusters[10,17].Itiseasytosee,particularlyinapplicationswithlargenumberoffeatures,thatvariouschoicesoffeaturesubsetswillrevealdifferentstructuresunderlyingthedata.Itisourconte

5、ntionthatthisinterplaybetweenthefeaturesubsetandthenumberofclustersisessentialtoprovideappropriateviewsofthedata.Wethusdefinetheproblemofmodelselectioninclusteringasselectingboththenumberofclustersandthefeaturesubset.Towardsthisendweproposeaunifiedobjectivefu

6、nctionwhoseargumentsincludetheboththefeaturespaceandnumberofclusters.Wethendescribetwoapproachestomodelselectionusingthisobjectivefunction.ThefirstapproachisbasedonaBayesianschemeusingthemarginallikelihoodformodelselection.Thesecondapproachisbasedonaschemeusi

7、ngcross-validatedlikelihood.Insection3weapplytheseapproachestodocumentclusteringbymakingassumptionsaboutthedocumentgenerationmodel.Further,fortheBayesianapproachwederiveaclosed-formsolutionforthemarginallikelihoodusingthisdocumentgenerationmodel.Wealsodescrib

8、eaheuristicforinitialfeatureselectionbasedonthedistributionalclusteringofterms.Section5describestheexperimentsandourapproachtovalidatetheproposedmodelsandalgorithms.Section6reportsanddisc