Canonical Correlation a Tutorial

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Canonical Correlationa TutorialMagnus BorgaJanuary 12, 2001Contents1 About this tutorial12 Introduction23 Definition24 Calculating Canonical correlations35 Relating difference between CCA and ordinary Correlation analysis . . to other linear subspace Equalnoiseenergies .................... between a signal and the corrupted signal . . .6A Affinetransformations ....................... Principal component analysis .................... Partial least Multivariate linear regression .................... 101 About this tutorialThis is a printable version of a Tutorial in HTML format. The Tutorial may bemodified at any time as will this version. The latest version of this Tutorial isavailable magnus/cca/.12 IntroductionCanonical Correlation analysis (CCA) is a way of measuring the linear relationshipbetween two multidimensional variables.

In this tutorial, correlation matrices are denoted R. The diagonal terms of C xx are the second order origin moments, E [x 2 i],of i. The diagonal terms in a covariance matrix are the variances or the second order central moments, E [(x i ) 2],of . The maximum likelihood estimator of is obtained by replacing the expecta-

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