From Multiblock Partial Least Squares to Multiblock Redundancy Analysis. A Continuum Approach

For the purpose of exploring and modelling the relationships between a dataset and several datasets, multiblock Partial Least Squares is a widely-used regression technique. It is designed as an extension of PLS which aims at linking two datasets. In the same vein, we propose an extension of Redundancy Analysis to the multiblock setting. We show that PLS and multiblock Redundancy Analysis aim at maximizing the same criterion but the constraints are different. From the solutions of both these approaches, it turns out that they are the two end points of a continuum approach that we propose to investigate.