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Title: The R package sparsePCA for block approaches and group-sparse PCA Authors:  Guy Chavent - INRIA-Paris (France)
Marie Chavent - University of Bordeaux (France) [presenting]
Abstract: Most of the algorithms developed in the recent years for sparse PCA aim at determining one single sparse principal component, and rely on the deflation process inherited from the unconstrained PCA when it comes to compute more than one sparse principal component. However, the use of the PCA deflation scheme in the sparse context where loadings and components are not necessarily orthogonal can lead to difficulties and joint optimization with respect to all loadings is expected to be more effective for variance maximization than sequential optimization. We will present a generalisation of the block sparse-$\ell_1$ algorithm to the case where sparsity is required to hold on group of variables rather than on the individual variables. We will also present the R package sparsePCA ( implementing block and deflation approaches for sparse and group-space PCA. We will then compare numerically the performance of block and deflation approaches for group-sparse PCA on simulated synthetic data and illustrate the influence of the group information on the retrieval of the sparsity pattern.