# SymNMF-Net for The Symmetric NMF Problem

arXiv: https://arxiv.org/abs/2205.13214 · HTML: https://mlsanity.com/paper/2205.13214/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 26 May 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Differentiable Linearized ADMM](https://mlsanity.com/paper/1905.06179/) (2019)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality](https://mlsanity.com/paper/1703.08267/) (2017)
- [Quartic First-Order Methods for Low-Rank Minimization](https://mlsanity.com/paper/1901.10791/) (2019)

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

- [Low-Rank Dependence Decomposition via Accelerated Symmetric Non-negative Matrix Factorization](https://mlsanity.com/paper/2607.24518/) (2026)

## Abstract (arXiv)

Recently, many works have demonstrated that Symmetric Non-negative Matrix Factorization~(SymNMF) enjoys a great superiority for various clustering tasks. Although the state-of-the-art algorithms for SymNMF perform well on synthetic data, they cannot consistently obtain satisfactory results with desirable properties and may fail on real-world tasks like clustering. Considering the flexibility and strong representation ability of the neural network, in this paper, we propose a neural network called SymNMF-Net for the Symmetric NMF problem to overcome the shortcomings of traditional optimization algorithms. Each block of SymNMF-Net is a differentiable architecture with an inversion layer, a linear layer and ReLU, which are inspired by a traditional update scheme for SymNMF. We show that the inference of each block corresponds to a single iteration of the optimization. Furthermore, we analyze the constraints of the inversion layer to ensure the output stability of the network to a certain extent. Empirical results on real-world datasets demonstrate the superiority of our SymNMF-Net and confirm the sufficiency of our theoretical analysis.