Structured Variable Selection for Regularized Generalized Canonical Correlation Analysis, The Multiple Facets of Partial Least Squares and Related Methods

Abstract : Regularized Generalized Canonical Correlation Analysis (RGCCA) extends regularized canonical correlation analysis to more than two sets of variables. Sparse GCCA (SGCCA) was recently proposed to address the issue of variable selection. However, the variable selection scheme offered by SGCCA is limited to the covariance (τ = 1) link between blocks. In this paper we go beyond the covariance link by proposing an extension of SGCCA for the full RGCCA model (τ ∈ [0, 1]). In addition, we also propose an extension of SGCCA that exploits pre-given structural relationships between variables within blocks. Specifically, we propose an algorithm that allows structured and sparsity-inducing penalties to be included in the RGCCA optimization problem.