Unsupervised multiblock data analysis: A unified approach and extensions

Abstract

For the analysis of multiblock data, a unified approach of several strategies such as Generalized Canonical Correlation Analysis (GCCA), Multiblock Principal Components Analysis (MB-PCA), Hierarchical Principal Components Analysis (H-PCA) and ComDim is outlined. These methods are based on the determination of global and block components. The unified approach postulates, on the one hand, two link functions that relate the block components to their associated global components and, on the other hand, two summing up expressions to compute the global components from their associated block components. Not only several well-known methods are retrieved but we also introduce a variant of GCCA. More generally, we hint to other possibilities of extensions thus emphasizing the fact that the unified approach, besides being simple, is versatile. We also show how this approach of analysis although basically unsupervised could be adapted to yield a supervised method to be used for a prediction purpose. Illustrations on the basis of simulated and real case studies are discussed.