Generalized constrained co-inertia analysis

In this paper a method for generalized constrained co-inertia analysis is proposed. This approach is based on a suitable decomposition of each set of variables which incorporates external information on both rows and columns of data matrices. These external information are incorporated in the analysis in order to improve the interpretability of the phenomenon under investigation. Once both matrices are decomposed according to the external information, we propose to apply the co-inertia analysis to any pair of obtainable submatrices in order to study relationships between them. A variety of existing and new extensions of COA are then realized. According to the nature of the data, this approach subsumes also several generalized constrained methods proposed in literature. An example is given to illustrate the proposed method.