# Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective

arXiv: https://arxiv.org/abs/2209.02528 · HTML: https://mlsanity.com/paper/2209.02528/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 6 Sep 2022.

## Builds on (most cited first, 6 of 6)

- [Deep Subspace Clustering Networks](https://mlsanity.com/paper/1709.02508/) (2017)
- [Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1811.05642/) (2018)
- [Spherical Principal Component Analysis](https://mlsanity.com/paper/1903.06877/) (2019)
- [Coordinate Descent Methods for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1509.01404/) (2015)
- [Inexact Block Coordinate Descent Methods For Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/1607.03092/) (2016)
- [Spherical Matrix Factorization](https://mlsanity.com/paper/2111.14536/) (2021)

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

- [Multi-Task Learning with Prior Information](https://mlsanity.com/paper/2301.01572/) (2023)
- [On Regularized Sparse Logistic Regression](https://mlsanity.com/paper/2309.05925/) (2023)
- [A Nonmonotone Gradient-Based Algorithm for Symmetric Nonnegative Matrix Factorization and Graph Clustering](https://mlsanity.com/paper/2606.02887/) (2026)

## Abstract (arXiv)

Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the similarity between data points. Most existing symmetric NMF algorithms require factor matrices to be nonnegative, and only focus on minimizing the gap between similarity matrix and its approximation for clustering, without giving a consideration to other potential regularization terms which can yield better clustering. In this paper, we explore factorizing a symmetric matrix that does not have to be nonnegative, presenting an efficient factorization algorithm with a regularization term to boost the clustering performance. Moreover, a more general framework is proposed to solve symmetric matrix factorization problems with different constraints on the factor matrices.