Principal Component Analysis with Noisy andor Missing Data带有噪声和_或缺失数据的主成分分析

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1、PUBLICATIONSOFTHEASTRONOMICALSOCIETYOFTHEPACIFIC,124:1015–1023,2012September©2012.TheAstronomicalSocietyofthePacific.Allrightsreserved.PrintedinU.S.A.PrincipalComponentAnalysiswithNoisyand/orMissingDataSTEPHENBAILEYPhysicsDivision,LawrenceBerkeleyNationalLaboratory,1Cyclo

2、tronRoad,Berkeley,CA,94720Received2012July10;accepted2012August17;published2012September19ABSTRACT.Wepresentamethodforperformingprincipalcomponentanalysis(PCA)onnoisydatasetswithmissingvalues.Estimatesofthemeasurementerrorareusedtoweighttheinputdatasuchthattheresultingeig

3、envectors,whencomparedtoclassicPCA,aremoresensitivetothetrueunderlyingsignalvariationsratherthanbeingpulledbyheteroskedasticmeasurementnoise.Missingdataaresimplylimitingcasesofweight¼0.Theunderlyingalgorithmisanoiseweightedexpectationmaximization(EM)PCA,whichhasadditional

4、benefitsofimplementationspeedandflexibilityforsmoothingeigenvectorstoreducethenoisecontribution.WepresentapplicationsofthismethodonsimulateddataandQSOspectrafromtheSloanDigitalSkySurvey(SDSS).Onlinematerial:colorfigures1.INTRODUCTIONobjectsatdifferentredshifts,andsomewave

5、lengthbinsmaybemaskedduetobrightskylinesorcosmicraycontamination.Principalcomponentanalysis(PCA)isapowerfulandwide-Missingdataareanextremecaseofnoisydata,wheremissinglyusedtechniquetoanalyzedatabyformingacustomsetofdataareequivalenttodatawithinfinitemeasurementvariance.“p

6、rincipalcomponent”eigenvectorsthatareoptimizedtode-ThisworkdescribesaPCAframeworkwhichincorporatesscribethemostdatavariancewiththefewestnumberofcom-estimatesofmeasurementvariancewhilesolvingfortheprin-ponents(Pearson1901;Hotelling1933;Jolliffe2002).Withthecipalcomponents.

7、Thisoptimizestheeigenvectorstodescribefullsetofeigenvectors,thedatamaybereproducedexactly;i.e.,thetrueunderlyingsignalvariationswithoutbeingundulyaf-PCAisatransformationthatcanlendinsightbyidentifyingfectedbyknownmeasurementnoise.Codewhichimplementswhichvariationsinacompl

8、exdatasetaremostsignificantandthisalgorithmisavailableathttps://github.com/sbailey/empca.howthey