# Heaviside Low-Rank Support Matrix Machine

arXiv: https://arxiv.org/abs/2603.00491 · HTML: https://mlsanity.com/paper/2603.00491/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 31 references that are in the map.
- First posted on arXiv 28 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Comprehensive Review On Twin Support Vector Machines](https://mlsanity.com/paper/2105.00336/) (2021)
- [Convergence results for projected line-search methods on varieties of low-rank matrices via Lojasiewicz inequality](https://mlsanity.com/paper/1402.5284/) (2014)
- [Bi-Sparse Unsupervised Feature Selection](https://mlsanity.com/paper/2412.16819/) (2024)
- [Normal Cones Intersection Rule and Optimality Analysis for Low-Rank Matrix Optimization with Affine Manifolds](https://mlsanity.com/paper/2202.08464/) (2022)
- [Support matrix machine: A review](https://mlsanity.com/paper/2310.19717/) (2023)
- [The Stochastic Conjugate Subgradient Algorithm For Kernel Support Vector Machines](https://mlsanity.com/paper/2407.21091/) (2024)
- [STAR-Net: An Interpretable Model-Aided Network for Remote Sensing Image Denoising](https://mlsanity.com/paper/2505.24327/) (2025)
- [A Counterexample for the Validity of Using Nuclear Norm as a Convex Surrogate of Rank](https://mlsanity.com/paper/1304.6233/) (2013)

## Abstract (arXiv)

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.