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1、NonlinearPrincipalComponentAnalysisUsingAutoassociativeNeuralNetworksMarkA.KramerLaboratoryforIntelligentSystemsinProcessEngineering,Dept.ofChemicalEngineering,MassachusettsInstituteofTechnology,Cambridge,MA02139Nonlinearprincipalcomponentanalysisisanoveltechniqueformultivariatedataanal
2、ysis,similartothewell-knownmethodofprincipalcomponentanalysis.NLPCA,likePCA,isusedtoidentifyandremovecorrelationsamongproblemvariablesasanaidtodimensionalityreduction,visualization,andexploratorydataanalysis.WhilePCAidentifiesonlylinearcorrelationsbetweenvariables,NLPCAuncoversbothlinea
3、randnonlinearcorrelations,withoutrestrictiononthecharacterofthenonlinearitiespresentinthedata.NLPCAoperatesbytrainingafeedforwardneuralnetworktoperformtheidentitymapping,wherethenetworkinputsarereproducedattheoutputlayer.Thenetworkcontainsaninternal“bottleneck”layer(containingfewernodes
4、thaninputoroutputlayers),whichforcesthenetworktodevelopacompactrepresentationoftheinputdata,andtwoadditionalhiddenlayers.TheNLPCAmethodisdemonstratedusingtime-dependent,simulatedbatchreactiondata.ResultsshowthatNLPCAsuccessfullyreducesdimensionalityandproducesafeaturespacemapresemblingt
5、heactualdistributionoftheunderlyingsystemparameters.introductionEngineersareoftenconfrontedwiththeproblemofextract-theidentificationtask(sincealeakisonlypossiblewhentheinginformationaboutpoorly-knownprocessesfromdata.Dis-netflowisnonzero)andreducesthedimensionalityofthecerningthesignifi
6、cantpatternsindata,asafirststeptoprocessrecognitionproblembysubstitutingasingleindicatorfortwounderstanding,canbegreatlyfacilitatedbyreducingdimen-ormoreindividualmeasurements.Ingeneral,selectionoffea-sionality.Thesuperficialdimensionalityofdata,orthenumberturessuchasthenetflowratedepen
7、dsontheultimateappli-ofindividualobservationsconstitutingonemeasurementvec-cation.However,incaseswheretheultimateapplicationoftor,isoftenmuchgreaterthantheintrinsicdimensionality,thedataisnotknowninadvance,asuitableobjectiveforthenumberofindependentvariablesunderlyingthesignifi
