# Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/1509.01404 · HTML: https://mlsanity.com/paper/1509.01404/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2015.

## Built on by (most cited first, 7 of 7)

- [Cyclic Block Coordinate Descent With Variance Reduction for Composite Nonconvex Optimization](https://mlsanity.com/paper/2212.05088/) (2022)
- [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)
- [Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective](https://mlsanity.com/paper/2209.02528/) (2022)
- [Randomized Algorithms for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2402.08134/) (2024)
- [Randomized Coordinate Subgradient Method for Nonsmooth Composite Optimization](https://mlsanity.com/paper/2206.14981/) (2022)
- [Symmetry Nonnegative Matrix Factorization Algorithm Based on Self-paced Learning](https://mlsanity.com/paper/2410.15306/) (2024)

## Abstract (arXiv)

Given a symmetric nonnegative matrix A, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix H, usually with much fewer columns than A, such that A ≈ HHT. SymNMF can be used for data analysis and in particular for various clustering tasks. In this paper, we propose simple and very efficient coordinate descent schemes to solve this problem, and that can handle large and sparse input matrices. The effectiveness of our methods is illustrated on synthetic and real-world data sets, and we show that they perform favorably compared to recent state-of-the-art methods.