# A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality

arXiv: https://arxiv.org/abs/1703.08267 · HTML: https://mlsanity.com/paper/1703.08267/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2017.

## Built on by (most cited first, 3 of 3)

- [A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2301.10499/) (2023)
- [Symmetric Sparse Boolean Matrix Factorization and Applications](https://mlsanity.com/paper/2102.01570/) (2021)
- [SymNMF-Net for The Symmetric NMF Problem](https://mlsanity.com/paper/2205.13214/) (2022)

## Abstract (arXiv)

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem. Furthermore, it achieves a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in parallel. Further, sufficient conditions are provided which guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real data sets suggest that the proposed algorithm converges quickly to a local minimum solution.