An Extension of Fast Iterative Shrinkage-thresholding to Riemannian Optimization for Sparse Principal Component Analysis

Authors

Wen Huang, Ke Wei

Abstract

Sparse PCA, an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the Riemannian optimization problem related to the ScoTLASS model for sparse PCA which can impose orthogonality and sparsity simultaneously. We extend FISTA from the Euclidean space to the Riemannian manifold to solve this problem. Since the optimization problem is essentially non-convex, a safeguard strategy is introduced in the algorithm. Numerical evaluations establish the computational advantages of the algorithm over the existing proximal gradient methods on manifold. Convergence of the algorithm to stationary points has also been rigorously justified.

Key words

Sparse PCA; Riemannian optimization; Stiefel manifold; Proximal gradient; FISTA;

Status

Numerical Linear Algebra with Applications, Accepted.

Download

Technical report: arxiv
Experiment code: zip

BibTex entry

Technical Report
@TECHREPORT{HW2021,
author = "Wen Huang and Ke Wei",
title = "An Extension of Fast Iterative Shrinkage-thresholding to Riemannian Optimization for Sparse Principal Component Analysis",
arxiv = "1909.05485",
year = 2021,
}