Transcription of Singular Value Decomposition & Independent …
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Singular Value Decomposition & Independent …
HST582 ,2005 IntroductionInthischapterwewillexamineho wwecangeneralizetheideaoftransforminga 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.
to analyze2, and in itself adds no information to the analysis.However, for a noise signal to carry no information, it must be white with a at spectrum and an autocorrelation function (ACF) equal to an impulse3.Most real noise is not really white, but colored in some respect. In fact, the term noise is often used rather loosely and is frequently used to …
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