Common canonical variates |
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| Authors: | NEUENSCHWANDER, BEAT E. FLURY, BERNARD D. |
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| Affiliation: | 1 Swiss Federal Office of Public Health, Division of Epidemiology Heβ-Straβe 27 E, 3097 Liebefeld, Switzerland
2 Department of Mathematics, Indiana University Rawles Hall, Bloomington, Indiana 47405, U.S.A. |
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| Abstract: | Canonical correlation analysis measures the linear relationshipbetween two random vectors X1 and X2 as the maximum correlationbetween linear combinations of X1 and linear combinations ofX2. Several generalisations of canonical correlation analysisto k2 random vectors X1 ..., Xk have been proposed in the literature(Kettenring, 1971, 1985), based on the principle of maximisingsome generalised measure of correlation. In this paper we proposean alternative generalisation, called common canonical variates,based on the assumption that the canonical variates have thesame coefficients in all k sets of variables. This generalisationis applicable in situations where all Xi have the same dimension.We present normal theory maximum likelihood estimation of commoncanonical variates, and illustrate their use on a morphometricdata set. |
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| Keywords: | Canonical correlation analysis Eigenvalue Eigenvector Maximum likelihood estimation Morphometric data Multivariate normal distribution Wishart distribution |
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