[2603.00491] Heaviside Low-Rank Support Matrix Machine

Computer Science > Machine Learning arXiv:2603.00491 (cs) [Submitted on 28 Feb 2026] Title:Heaviside Low-Rank Support Matrix Machine Authors:Xianchao Xiu, Shenghao Sun, Xinrong Li, Jiyuan Tao View a PDF of the paper titled Heaviside Low-Rank Support Matrix Machine, by Xianchao Xiu and 3 other authors View PDF Abstract:Support matrix machine (SMM) is an emerging classification framework that directly handles matrix-structured observations, thereby avoiding the spatial correlations destroyed by vectorization. However, most existing SMM variants rely on convex or nonconvex surrogate loss functions, which may lead to high sensitivity to noise. To address this issue, we propose a novel Heaviside low-rank SMM model called HL-SMM, which leverages the Heaviside loss instead of the common hinge or ramp losses for robustness. Moreover, the low-rank constraint is adopted to accurately characterize the inherent global structure. In theory, we analyze the Karush-Kuhn-Tucker (KKT) points and rigorously prove the sufficient and necessary conditions. In algorithms, we develop an effective proximal alternating minimization (PAM) scheme, where all subproblems have closed-form solutions. Extensive experiments on benchmark datasets validate that the proposed HL-SMM achieves superior classification accuracy and robustness compared to state-of-the-art methods. Subjects: Machine Learning (cs.LG); Optimization and Control (math.OC) Cite as: arXiv:2603.00491 [cs.LG]   (or arXiv:2603.00491v1 [cs.LG...