Robust and Globally Sparse Pca via Majorization-Minimization and Variable Splitting

Hugo Brehier; Arnaud Breloy; Mohammed Nabil El Korso; Sandeep Kumar

ICASSP 2023accepted0 citations

Robust and Globally Sparse Pca via Majorization-Minimization and Variable Splitting

Hugo Brehier, Arnaud Breloy, Mohammed Nabil El Korso, Sandeep Kumar

Abstract

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.

BibTeX

@inproceedings{icassp2023_robustandgloball,
  title = {Robust and Globally Sparse Pca via Majorization-Minimization and Variable Splitting},
  author = {Hugo Brehier and Arnaud Breloy and Mohammed Nabil El Korso and Sandeep Kumar},
  booktitle = {ICASSP 2023},
  year = {2023}
}