There exist several extensions of canonical correlation analysis that allow the analysis of data on more than two sets of variables. Carroll's (1968) generalized canonical correlation analysis (GCCA) is one such extension. Advantages of Carroll's GCCA approach are the easiness of computation and the fact that it takes the classical two-variable method as a special case. This last property is not trivial as, unlike the classical two sets method, the generalized approach does not explicitly place a constraint on the canonical variates. We will show that when applied to two sets of variables, Carroll's GCCA yields orthogonal canonical variates equivalent to those obtained classical canonical correlation analysis. However, when there are more than two sets of variables, the obtained canonical variates are typically not orthogonal. In this paper, we propose an alternative to Carroll's generalization that always yields orthogonal canonical variates and that takes classical canonical correlation analysis as a special case.

References:

Carroll, J. Douglas (1968), “Generalization of Canonical Correlation Analysis to Three or More Sets of Variables,” Proceedings of the 76^th Annual Convention of the American Psychological Association, volume 3, 227-228.

Keywords: Generalized canonical correlation analysis; Multiple sets

Biography: Michel van de Velden is an assistant professor at the Econometric Institute of the Erasmus University Rotterdam. His research interests concern development and application of visualization methods for multivariate data.