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Singular Value Decomposition & Independent Component ...

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HST582 ,2005IntroductionInthischapterwewillexam inehowwecangeneralizetheideaoftransformi nga timeseriesinanalternativerepresentation, suchastheFourier(frequency)domain,tofaci li-tatesystematicmethodsofeitherremoving ( ltering)oradding(interpolating) , wewillexaminethetechniquesofPrincipalCom ponentAnalysis(PCA)usingSingularValueDec omposition(SVD),andIndependentComponentA nalysis(ICA).Bothofthesetechniquesutiliz ea representationofthedataina statisticaldomainratherthana ,thedatais projectedontoa newsetofaxesthatful llsomestatisticalcriterion,whichimplyind ependence,ratherthana thattheFouriercomponentsontowhicha datasegmentis projectedare xed, If thestructureofthedatachangesovertime,the ntheaxesontowhichthedatais essentiallya methodforseparatingthedataoutintoseparat esourceswhichwillhopefullyallowustoseeim portantstructureina ,bycalculatingthepowerspectrumofa segmentofdata, (amplitudesquared)alongcertainfrequencyv ectorsis thereforehigh,meaningwehavea strongcomponentinthesignal1atthatfrequen cy.

HST582J/6.555J/16.456J Biomedical Signal and Image Processing Spring 2005 Singular Value Decomposition & Independent Component Analysis for Blind Source Separation

  Separation

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