An Improved Method for Generalized Constrained Canonical Correlation Analysis

We propose an improved method for generalized constrained canonical correlation analysis (GCCANO). In GCCANO, data matrices are first decomposed into several submatrices according to some external information on rows and columns of the data matrices. Decomposed matrices are then subjected to canonical correlation analysis (CANO). However, orthogonal decompositions of data matrices do not necessarily entail the corresponding decompositions of projectors defined by the data matrices. Consequently, no additive partitioning of the total redundancy between two sets of variables was possible in the original GCCANO. In this paper we introduce two orthogonal decompositions of projectors that allow additive partitionings of the total redundancy. Terms in the decompositions have straightforward interpretations. We develop an improved method for GCCANO based on the new decompositions, while preserving the most important features of the original GCCANO. An example is given to illustrate the proposed method