l0 Factor Analysis: A P-Stationary Point Theory

• 成果类型: Article
• 署名作者: Wang, Linyang; Zhu, Bin; Liu, Wanquan
• 署名单位: Sun Yat Sen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3552869
• 发表日期: 2025
• 页码: 6050-6063
• 关键词: Covariance matrices; optimization; vectors; Sparse matrices; Eigenvalues and eigenfunctions; Convex functions; CONVERGENCE; Principal Component Analysis; Matrix decomposition; linear programming; l(0) norm; Alternating direction method of multipliers (ADMM); factor analysis (FA); low-rank plus sparse matrix decomposition; nonconvex nonsmooth optimization

摘要

Factor analysis is a widely used modeling technique for stationary time series, which achieves dimensionality reduction by revealing a hidden low-rank plus sparse structure of the covariance matrix. Such an idea of parsimonious modeling has also been important in the field of systems and control. In this article, a nonconvex nonsmooth optimization problem involving the l(0) norm is constructed in order to achieve the low-rank and sparse additive decomposition of the sample covariance matrix. We establish the existence of an optimal solution and characterize these solutions via the concept of proximal stationary points. Furthermore, an ADMM algorithm is designed to solve the l(0) optimization problem, and a subsequence convergence result is proved under reasonable assumptions. Finally, numerical experiments demonstrate the effectiveness of our method in comparison with some alternatives in the literature.