Connections between multiple co-inertia analysis and consensus principal component analysis

Consensus Principal Component Analysis is a multiblock method which is designed to reveal covariant patterns between and within several multivariate data sets. The computation of the parameters of this method namely, block scores, block loadings, global loadings and global scores are based on an iterative procedure. However, very few properties are known regarding the convergence of this iterative procedure. The paper discloses a monotony property of CPCA and exhibits an optimisation criterion for which CPCA algorithm provides a monotonic convergent solution. This makes it possible to highlight new properties of this method of analysis and pinpoint its connection to existing methods such as Generalized Canonical Correlation Analysis and Multiple Co-inertia Analysis.