基于多元t分布的概率主成分分析及其應用.pdf

1、東南大學碩士學位論文基于多元t分布的概率主成分分析及其應用姓名：趙建華申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：江其保20021101東南大學碩士學位論文ABSTRACTPrincipalcomponentanalysis(PCA)isapopulartechniqueindimensionreductionSinceLllescopeofitsapplicationislimitedbyitsgloballinearityse

2、veralgeneralizationsareproposedrecentlyintheliteratureTileprobabilisticPCA，introducedbyTippingandBishopf39，401andtermedasGaussian—PP刪here，isaparticularlyimportantoueofsucheffortInthisthesis；wederiveprobabilisticPCA，which

3、wecallittPPGAlfordatasampledftomthefinitemixtureofmultivariatetdistributions，wherebyweobtainanewgeneral—purposedimensionreductionalgorithmwhichisofsomeimportanceinbotbtheoryandapplicationOurmaincontributionsaresummarized

4、aswhatfollows：TheoreticahSupposedataweresampledfronlamixtureofmdvariatetdistribu—tions；andeachmixingcomponentsatisfiesanisotropicfactoranalysismodel(see321)Inchapters3and4，wederivedthemaximumlikelihoodestimationofthemode

5、lparametersbyusingtheEMtypealgorithm，whichprovidesUSanewdataprojectionandreconstructionalgorithm，ie，tPPCAWhenthe‘degreeoffreedon：Is’Ⅳ=ootPPCAi8exactlytheGanssian—PPCAInthecasem=1theprojectionisgivenbytheprincipalcomponen

6、tdecompositionofamatrixS7(see31)，whichisreducedtothesamplecovariancematrixSonlywhen∥=。oThisshowsthattheusuaIPCAiSadequateonlyfornormaldataApplications：AsdataismodelledasfinitemixtureoftdistributionstPPCAisrobustinapplica

7、tionComparingwiththeuseofGaussiandistribution，ourapproachdoesgivebetterresultsasisshownbytheexperimentsinchapter5TheexperimentonhandwrittenEnglishletterrecognitionin51showsthattheerrorrateoft—PPCAissignificantlysmallerth

8、anthatofGanssianPPCA(seeTable51)WerecognizedfrombothtablesthatdataprojectionmaybenecessarybeforeclassificationThisphenomenoniS1efttothefuturestudyIntheexperimentondatacompressionin52，bycomparingF逗52with53，thequalityofthe