ON GENERALIZED CANONICAL CORRELATION ANALYSIS

discussed and compared in Kettenring (1971) and Gower (1989). In this paper, we shall concern ourselves with the generalization proposed by Carroll (1968). Carroll’s approach has some attractive properties that makes the method well …t for the analysis of multiple-set data. First of all, computationally, the method is straightforward as its solution is based on an eigenequation. Secondly, the method is closely related to several well-known multivariate techniques. In particular, principal component analysis and multiple correspondence analysis. Thirdly, Carroll’s generalization takes ordinary canonical correlation analysis as a special case. Although this last property is well known and already mentioned by Carroll (1968), a formal proof in the context of generalized canonical correlation analysis is not easy to …nd in the literature. Ten Berge (1979) does provide a proof in the context of factor rotation. In this paper, we will present a new proof of the equivalence. In addition, we propose a new generalized canonical correlation analysis approach that takes classical canonical correlationa analysis as a special case and always yields orthogonal canonical variates. Canonical Correlation Analysis In canonical correlation analysis (CCA), Hotelling (1936) the aim is to …nd linear combinations for two sets of variables in such a way that the correlation between the two linear combinations is