Current multiblock methods: Competition or complementarity? AÂ comparative study in a unified framework

We address the issue of exploring-with respect to multiple regression model(s) or to simple pairwise links-the relationships between blocks of variables measured on the same observations. Multiblock methods have been developed over the past twenty years, and are now used more and more frequently, especially for high-dimensional data. We focus on three current methods: regularized Generalized Structured Component Analysis (rGSCA), regularized Generalized Canonical Correlation Analysis (rGCCA) and THEmatic Model Exploration (THEME). These methods are rewritten in a common formal setting and compared with respect to two issues: how they explore block-relationships, and how they separate information from noise. Multiblock methods are applied to simulated data and to real data pertaining to the chemistry framework to illustrate their differences and complementarities.