Common canonical variates

Canonical correlation analysis measures the linear relationship between two random vectors X 1 and X 2 as the maximum correlation between linear combinations of X 1 and linear combinations of X 2 . Several generalisations of canonical correlation analysis to k > 2 random vectors X 1 ,...,X k have been proposed in the literature (Kettenring, 1971, 1985), based on the principle of maximising some generalised measure of correlation. In this paper we propose an alternative generalisation, called common canonical variates, based on the assumption that the canonical variates have the same coefficients in all k sets of variables. This generalisation is applicable in situations where all X i have the same dimension. We present normal theory maximum likelihood estimation of common canonical variates, and illustrate their use on a morphometric data set.