# A Review of Nonnegative Matrix Factorization Methods for Clustering

arXiv: https://arxiv.org/abs/1507.03194 · HTML: https://mlsanity.com/paper/1507.03194/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2015.

## Built on by (most cited first, 2 of 2)

- [Privacy-Preserving Distributed Nonnegative Matrix Factorization](https://mlsanity.com/paper/2403.18326/) (2024)
- [Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization](https://mlsanity.com/paper/2104.12289/) (2021)

## Abstract (arXiv)

Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that they are closely linked. In this report, we provide a gentle introduction to clustering and NMF before reviewing the theoretical relationship between them. We then explore several NMF variants, namely Sparse NMF, Projective NMF, Nonnegative Spectral Clustering and Cluster-NMF, along with their clustering interpretations.