Alternating minimization for square root principal component pursuit

• URL: http://arxiv.org/abs/2501.00471v1
• Date: Tue, 31 Dec 2024 14:43:50 GMT
• Title: Alternating minimization for square root principal component pursuit
• Authors: Shengxiang Deng, Xudong Li, Yangjing Zhang,
• Abstract summary: We develop efficient algorithms for solving the square root principal component pursuit (SRPCP) problem.<n>Specifically, we propose a tuning-free alternating minimization (AltMin) algorithm, where each iteration involves subproblems enjoying closed-form optimal solutions.<n>We introduce techniques based on the variational formulation of the nuclear norm and Burer-Monteiro decomposition to further accelerate the AltMin method.
• Score: 2.449191760736501
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recently, the square root principal component pursuit (SRPCP) model has garnered significant research interest. It is shown in the literature that the SRPCP model guarantees robust matrix recovery with a universal, constant penalty parameter. While its statistical advantages are well-documented, the computational aspects from an optimization perspective remain largely unexplored. In this paper, we focus on developing efficient optimization algorithms for solving the SRPCP problem. Specifically, we propose a tuning-free alternating minimization (AltMin) algorithm, where each iteration involves subproblems enjoying closed-form optimal solutions. Additionally, we introduce techniques based on the variational formulation of the nuclear norm and Burer-Monteiro decomposition to further accelerate the AltMin method. Extensive numerical experiments confirm the efficiency and robustness of our algorithms.

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