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Arbeitsgruppe Bülthoff - Face Rec

Max-Planck-Institutf r biologische KybernetikSpemannstra e 38 72076 T bingen GermanyArbeitsgruppe B lthoffTechnicalReportNo December NonlinearComponentAnalysisasaKernelEigen valueProblemBernhardSch olkopf AlexanderSmola andKlaus RobertM ullerAbstractWedescribeanewmethodforperf orminganonlinearformofPrincipalComponent Anal ysis Bytheuseofintegraloperatorkernelfunction s wecane cientlycomputeprincipalcomponentsinhigh dimensionalfeaturespaces relatedtoinputspacebysomenonlinearmap forinstancethespaceofallpossible pixelproductsin images Wegivethederivationofthemethod alongwithadiscussionofothertechniqueswhi chcanbemadenonlinearwiththekernelapproac h andpresent rstexperimentalresultsonnonlinearfea tureextractionforpatternrecognition ASandKRMarewithGMDF irst ForschungszentrumInformationstechnik RudowerChaussee Berlin ASandBSweresupportedbygrantsfromtheStudi enstiftungdesdeutschenVolkes BSthankstheGMDF irstforhospitalityduringtwovisits ASandBSthankV Vapnikforintroducingthemtokernelrepresen tationsofdotproductsduringjointworkonSup portVectormachines Thisworkpro tedfromdiscussionswithV Blanz L Bottou C Burges H B ultho K Gegenfurtner P Ha ner N Murata P Simard S Solla V Vapnik andT Vetter WearegratefultoV Blanz C Burges andS Sollaforreadingapreliminaryversionofthem anuscript Th

In tro duction Principal Comp onen t Analysis PCA is a p o w er ful tec hnique for extracting structure from p ossi bly highdimensional data sets It is readily p er

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