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Singular Value Decomposition & Independent …

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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)alongc

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

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