An improved method for generalized constrained canonical correlation analysis

An improved method for generalized constrained canonical correlation analysis (GCCANO) is proposed. In the original GCCANO, data matrices were first decomposed into the sum of several matrices according to some external information on rows and columns of the data matrices. Decomposed matrices were then subjected to canonical correlation analysis (CANO). However, orthogonal decompositions of data matrices do not necessarily entail orthogonal decompositions of projectors defined by the data matrices. This latter property is crucial in additive partitionings of the total association between two sets of variables. Consequently, no additive partitionings of the total association was possible in the original GCCANO. In this paper two orthogonal decompositions of projectors were proposed that allow additive partitionings of the total association. Terms in the decompositions have straightforward interpretations. An improved method for GCCANO is developed based on the decompositions, while preserving the most important features of the original method. An example is given to illustrate the proposed method.