資源描述：
《Principal Component Analysis with Noisy andor Missing Data帶有噪聲和_或缺失數(shù)據(jù)的主成分分析》由會(huì)員上傳分享，免費(fèi)在線(xiàn)閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫(kù)。
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.Missingdataaresimplylimitingcasesofweight?0.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
