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1、NeuralNetworksPERGAMONNeuralNetworks13(2000)411±430www.elsevier.com/locate/neunetInvitedarticleIndependentcomponentanalysis:algorithmsandapplicationsA.Hyvaèrinen,E.Oja*NeuralNetworksResearchCentre,HelsinkiUniversityofTechnology,P.O.Box5400,FIN-02015HUT,Helsinki,FinlandReceived2
2、8March2000;accepted28March2000AbstractAfundamentalprobleminneuralnetworkresearch,aswellasinmanyotherdisciplines,is?ndingasuitablerepresentationofmultivariatedata,i.e.randomvectors.Forreasonsofcomputationalandconceptualsimplicity,therepresentationisoftensoughtasalineartransforma
3、tionoftheoriginaldata.Inotherwords,eachcomponentoftherepresentationisalinearcombinationoftheoriginalvariables.Well-knownlineartransformationmethodsincludeprincipalcomponentanalysis,factoranalysis,andprojectionpursuit.Independentcomponentanalysis(ICA)isarecentlydevelopedmethodin
4、whichthegoalisto?ndalinearrepresentationofnon-Gaussiandatasothatthecomponentsarestatisticallyindependent,orasindependentaspossible.Sucharepresentationseemstocapturetheessentialstructureofthedatainmanyapplications,includingfeatureextractionandsignalseparation.Inthispaper,weprese
5、ntthebasictheoryandapplicationsofICA,andourrecentworkonthesubject.q2000PublishedbyElsevierScienceLtd.Keywords:Independentcomponentanalysis;Projectionpursuit;Blindsignalseparation;Sourceseparation;Factoranalysis;Representation1.MotivationcouldlooksomethinglikethoseinFig.1andthem
6、ixedsignalscouldlooklikethoseinFig.2.TheproblemistoImaginethatyouareinaroomwheretwopeoplearerecoverthedatainFig.1usingonlythedatainFig.2.speakingsimultaneously.Youhavetwomicrophones,Actually,ifweknewtheparametersaij,wecouldsolvewhichyouholdindifferentlocations.Themicrophonesthe
7、linearequationin(1)byclassicalmethods.Thepointis,giveyoutworecordedtimesignals,whichwecoulddenotehowever,thatifyoudonotknowtheaij,theproblemisbyx1(t)andx2(t),withx1andx2theamplitudes,andttheconsiderablymoredif?cult.timeindex.EachoftheserecordedsignalsisaweightedsumOneapproachto
8、solvingthisproblemwouldbetouseofthespeechsignalsemitte
