# An Efficient Alternating Algorithm for ReLU-based Symmetric Matrix Decomposition

arXiv: https://arxiv.org/abs/2503.16846 · HTML: https://mlsanity.com/paper/2503.16846/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 9 of 9)

- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems](https://mlsanity.com/paper/1702.02505/) (2017)
- [First Order Methods beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems](https://mlsanity.com/paper/1706.06461/) (2017)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization](https://mlsanity.com/paper/1904.03537/) (2019)
- [Accelerated Algorithms for Nonlinear Matrix Decomposition with the ReLU function](https://mlsanity.com/paper/2305.08687/) (2023)
- [Multiplicative Noise Removal: Nonlocal Low-Rank Model and Its Proximal Alternating Reweighted Minimization Algorithm](https://mlsanity.com/paper/2002.07633/) (2020)
- [A Momentum Accelerated Algorithm for ReLU-based Nonlinear Matrix Decomposition](https://mlsanity.com/paper/2402.02442/) (2024)
- [An Accelerated Alternating Partial Bregman Algorithm for ReLU-based Matrix Decomposition](https://mlsanity.com/paper/2503.02386/) (2025)

## Built on by (most cited first, 1 of 1)

- [Subzero matrix completion for sparse data analysis: large-scale learning of latent low-rank structure](https://mlsanity.com/paper/2608.21607/) (2026)

## Abstract (arXiv)

Symmetric matrix decomposition is an active research area in machine learning. This paper focuses on exploiting the low-rank structure of non-negative and sparse symmetric matrices via the rectified linear unit (ReLU) activation function. We propose the ReLU-based nonlinear symmetric matrix decomposition (ReLU-NSMD) model, introduce an accelerated alternating partial Bregman (AAPB) method for its solution, and present the algorithm's convergence results. Our algorithm leverages the Bregman proximal gradient framework to overcome the challenge of estimating the global L-smooth constant in the classic proximal gradient algorithm. Numerical experiments on synthetic and real datasets validate the effectiveness of our model and algorithm.