ROBUST AND GLOBALLY SPARSE PCA VIA MAJORIZATION-MINIMIZATION AND VARIABLE SPLITTING

Hugo Brehier (1) , Arnaud Breloy (2) , Mohammed Nabil El Korso (3) , Sandeep Kumar (4)

1 SONDRA - Sondra, CentraleSupélec, Université Paris-Saclay
2 LEME - Laboratoire Energétique Mécanique Electromagnétisme
3 L2S - Laboratoire des signaux et systèmes
4 IIT Delhi - Indian Institute of Technology Delhi

This paper addresses the problem of robust and sparse PCA. We consider a formulation combining a M-estimation type robust subspace recovery term and a mixed norm that promotes structured sparsity in the basis vectors, which is especially interesting for joint dimension reduction and variable selection. To solve it, we propose to leverage variable splitting methods, with the crucial step then lying on the Stiefel manifold. The resolution of this subproblem, involving the orthonormality constraint, is achieved through a tailored majorization-minimization (MM) step. Numerical experiments on gene expression measurements illustrate the interest of the proposal.

Mots clés: Sparse PCA Robust Subspace Recovery Stiefel Manifold ADMM Majorization-Minimization; Sparse PCA; Robust Subspace Recovery; Stiefel Manifold; ADMM; Majorization-Minimization

Domaines: Sciences de l'ingénieur [physics]

Hugo Brehier, Arnaud Breloy, Mohammed Nabil El Korso, Sandeep Kumar. ROBUST AND GLOBALLY SPARSE PCA VIA MAJORIZATION-MINIMIZATION AND VARIABLE SPLITTING. ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Jun 2023, Rhodes Island, France. ⟨10.1109/ICASSP49357.2023.10094882⟩. ⟨hal-04399125⟩