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

Tommy Lofstedt (1) , Fouad Hadj-Selem (1) , Vincent Guillemot (1) , Cathy Philippe (2) , Edouard Duchesnay (3) , Vincent Frouin (1) , Arthur Tenenhaus (4)

1 NEUROSPIN - Service NEUROSPIN
2 UMR 8203 - Vectorologie et thérapeutiques anti-cancéreuses [Villejuif]
3 UNATI - Unité Analyse et Traitement de l'Information
4 L2S - Laboratoire des signaux et systèmes

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.

Domains: Engineering Sciences [physics]; Signal and Image processing

Tommy Lofstedt, Fouad Hadj-Selem, Vincent Guillemot, Cathy Philippe, Edouard Duchesnay, et al.. Structured Variable Selection for Regularized Generalized Canonical Correlation Analysis, The Multiple Facets of Partial Least Squares and Related Methods . Springer Proceedings in Mathematics & Statistics, pp.129-139, 2016, The Multiple Facets of Partial Least Squares and Related Methods, ⟨10.1007/978-3-319-40643-5_10⟩. ⟨hal-01396614⟩