Chapter20CanonicalCorrelationandCorrespondingAnalysis20.1CanonicalCorrelation

20.1.1Definitionofcanonicalcorrelationvariables

20.1.3CanonicalCorrelationStructures

20.1.4

RotationofCanonicalVariablesandAdjustedCanonicalCorrelationCoefficient

20.1.5RedundancyofCanonicalVariables

20.1.6RegressiononCanonicalVariables

20.2CorrespondenceAnalysis

20.2.1ComputationProcedure

(2)Calculationoftwocorrelationmatrices

Rowpairwisecorrelationcoefficients:correlationcoefficientmatrixA.Columnpairwisecorrelationcoefficients:correlationcoefficientmatrixB.AandBhaveidenticalnon-zeroeigenvalues,butdifferenteigenvectors

Example:Non-zeroeigenvalues:0.1992,0.03009,0.0008595.Ratesofcontribution:86.56%,13.07%,0.37%.20.2.2Application–AnalysisofContraceptiveMethodsUsebyVariousGroupsofPeople

20.2.4RelationshipbetweenCorrespondenceAnalysisandCanonicalCorrelationAnalysis

ToperformcanonicalcorrelationanalysisonXvariables(roweffects)andYvariables(columneffects),getthreecanonicalcoefficients0.446368,0.173455,0.029317squaredcoefficients0.199245,0.030087,0.000859----eigenvaluesincorrespondenceanalysis.CanonicalcorrelationanalysisemphasizesoncanonicalvariablesandcanonicalcorrelationcoefficientsCorrespondenceanalysisattemptstointerpretthecontingencytablestructure.20.3CanonicalDiscriminantAnalysis

Discriminationproblemforkpopulations:

Trainingsample:ksamplesfromk

2populations.ObservationsfromX1,X2,…,Xp,p＞kSamp