mclachlan, geoffrey and david peel_finite mixture models

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1、ContentsPrefacexix1GeneralIntroduction11.1Introduction11.1.1FlexibleMethodofModeling11.1.2InitialApproachtoMixtureAnalysis21.1.3ImpactofEMAlgorithm31.2OverviewofBook41.3BasicDefinition61.4InterpretationofMixtureModels71.5ShapesofSomeUnivariateNormalMixtures91.5.1MixturesofTwoNormal

2、HomoscedasticComponents91.5.2MixturesofUnivariateNormalHeteroscedasticComponents111.6ModelingofAsymmetricalData141.7NormalScaleMixtureModel171.8SpuriousClusters171.9Incomplete-DataStructureofMixtureProblem191.10SamplingDesignsforClassifiedData211.11ParametricFormulationofMixtureMod

3、el22vllVlilCONTENTS1.12NonparametricMLEstimationofaMixingDistribution231.13EstimationofMixtureDistributions241.14IdentifiabilityofMixtureDistributions261.15ClusteringofDataviaMixtureModels291.15.1MixtureLikelihoodApproachtoClustering291.15.2Decision-TheoreticApproach301.15.3Cluster

4、ingofI.I.D.Data311.15.4ImageSegmentationorRestoration321.16HiddenMarkovModels331.17TestingfortheNumberofComponentsinMixtureModels341.18BriefHistoryofFiniteMixtureModels351.19Notation372MLFittingofMixtureModels402.1Introduction402.2MLEstimation402.3InformationMatrices412.4Asymptotic

5、CovarianceMatrixofMLE422.5PropertiesofMLEsforMixtureModels422.6ChoiceofRoot442.7TestforaConsistentRoot442.7.1BasisofTest442.7.2Example2.1:LikelihoodFunctionwithTwoMaximizers452.7.3FormulationofTestStatistic452.8ApplicationofEMAlgorithmforMixtureModels472.8.1DirectApproach472.8.2For

6、mulationasanIncomplete-DataProblem482.8.3E-Step482.8.4M-Step492.8.5AssessingtheImpliedErrorRates502.9FittingMixturesofMixtures512.10MaximumaPosterioriEstimation522.11AnAitkenAcceleration-BasedStoppingCriterion522.12StartingValuesforEMAlgorithm542.12.1SpecificationofanInitialParamet

7、erValue542.12.2RandomStartingValues55CONTENTSIX2.12.3Example2.2:SyntheticDataSet1562.12.4DeterministicAnnealingEMAlgorithm572.13StochasticEMAlgorithm612.14RateofConvergenceoftheEMAlgorithm612.14.1RateMatrixforLinearConvergence612.14.2RateMatrixinTermsofInformationMatrices622.15Info

8、rmationMatrixforMixtureMod