Supervised Strategies of Multiblock Data Analysis: A Unified Approach and Extension

Within the framework of multiblock data analysis, a unified approach of supervised methods is discussed. It encompasses multiblock redundancy analysis (MB-RA) and multiblock partial least squares (MB-PLS) regression. Moreover, we develop new supervised strategies of multiblock data analysis, which can be seen as variants of one or the other of these two methods. They are respectively refered to as multiblock weighted redundancy analysis (MB-WRA) and multiblock weighted covariate analysis (MB-WCov). The four methods are based on the determination of latent variables associated with the various blocks of variables. They are derived from clear optimization criteria whose aim is to maximize either the sum of the covariances or the sum of squared covariances between the latent variable associated with the response block of variables and the block latent variables associated with the various explanatory blocks of variables. We also propose indices to help better interpreting the outcomes of the analyses. The methods are illustrated and compared based on simulated and real datasets.