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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 Thisw

Max-Planck-Institut für biologische Kybernetik Spemannstraße 38 • 72076 Tübingen • Germany Arbeitsgruppe Bülthoff T ec hnical Rep ort No Decem

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