Canonical Correlation Analysis Formulated as Maximizing Sum of Squared Correlations and Rotation of Structure Matrices

Abstract

In this paper, we propose a new formulation of canonical correlation analysis, which is equivalent to the existing one. Under the new formulation, two canonical structure matrices have freedom of orthogonal rotation. We thus propose an orthogonal rotation method for rotating two structure matrices individually to simple structures. This method is different from the one derived from the existing formulation which only allows the simultaneous rotation of two structure matrices. It is illustrated that our proposed method facilitates the interpretation of solutions of canonical correlation analysis in a real data example.