Principal Component Analysis

approximation assumptions biplot Chapter cluster analysis coefficients columns Component number Contrasts correlation matrix correspondence analysis covariance matrix covariance or correlation criterion cut-off data set defined deleted described diagram dimensionality dimensions discussed in Section distribution eigenvalues eigenvectors equal equation equivalent estimates Euclidean distance example factor analysis factor model Figure four PCs give given interpretation ith observation Jolliffe jth variable kth PC large number last few PCs linear functions Mahalanobis distance maximized methods multivariate normality original variables orthogonal orthogonal matrix outliers painters PC regression PCs account population positive possible predictor variables principal co-ordinate analysis Principal component analysis procedure Property q PCs relationships retained rotation rule sample covariance sample PCs scores scree scree graph second PC similar similarity matrix singular value decomposition statistical structure Table techniques three PCs tion total variation two-dimensional uncorrelated values variable selection variances vectors x₁ zero