Canonical Correlationa Tutorial

Canonical Correlationa TutorialMagnus BorgaJanuary 12, 2001Contents1 About this tutorial 12 Introduction 23 Definition 24 Calculating canonical correlations 35 Relating topics 35.1 The difference between CCA and ordinary correlation analysis . . 35.2 Relationtomutualinformation................... 45.3 Relation to other linear subspace methods ....... 45.4 RelationtoSNR........................... 55.4.1 Equalnoiseenergies... 55.4.2 Correlation between a signal and the corrupted signal . . . 6A Explanations 6A.1Anoteoncorelationandcovariancematrices........... 6A.2Affinetransformations ................. 6A.3Apieceofinformationtheory......... 7A.4 Principal component analysis . ............. 9A.5 Partial least squares .............. 9A.6 Multivariate linear regression . ............. 9A.7Signaltonoiseratio.............. 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 athttp://people.imt.liu.se/˜magnus/cca/.1[wxi][2Tyy[[Ew][2yxxy[:Ew>^ETxyx=]yETwxxiwT^xjTTxC=wxEyyyyyT]^Ewwyyy]T=wwCTxx[Cixyjw=y[qTwxyTwxTCCxxww6xTw=2 IntroductionCanonical correlation ...