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Canonical Correlation a Tutorial

Canonical Correlationa TutorialMagnus BorgaJanuary 12, 2001 Contents1 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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