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MATLABCODEFORPCAbyJonathonShlens(SalkInstituteforBiologicalSciences)http://www.snl.salk.edu/~shlens/pub/notes/pca.pdfThisfirstversionfollowsSection5(ofabovetutorial)byexaminingthecovarianceofthedataset.function[signals,PC,V]=pca1(data)%PCA1:PerformPCAusingcovariance.%data-MxNmatrixofinputdata%(Mdimensions,Ntrials)%signals-MxNmatrixofprojecteddata%PC-eachcolumnisaPC%V-Mx1matrixofvariances[M,N]=size(data);%subtractoffthemeanforeachdimensionmn=mean(data,2);data=data-repmat(mn,1,N);%calculatethecovariancematrixcovariance=1/(N-1)*data*data’;%findtheeigenvectorsandeigenvalues[PC,V]=eig(covariance);%extractdiagonalofmatrixasvectorV=diag(V);%sortthevariancesindecreasingorder[junk,rindices]=sort(-1*V);V=V(rindices);PC=PC(:,rindices);%projecttheoriginaldatasetsignals=PC’*data;ThissecondversionfollowsSection6computingPCAthroughSVD.function[signals,PC,V]=pca2(data)%PCA2:PerformPCAusingSVD.%data-MxNmatrixofinputdata%(Mdimensions,Ntrials)%signals-MxNmatrixofprojecteddata%PC-eachcolumnisaPC%V-Mx1matrixofvariances[M,N]=size(data);%subtractoffthemeanforeachdimensionmn=mean(data,2);data=data-repmat(mn,1,N);%constructthematrixYY=data’/sqrt(N-1);%SVDdoesitall[u,S,PC]=svd(Y);%calculatethevariancesS=diag(S);V=S.*S;%projecttheoriginaldatasignals=PC’*data;
