A Review of Nonnegative Matrix Factorization Methods for Clustering

TL;DR

This paper reviews the relationship between Nonnegative Matrix Factorization (NMF) and clustering, discussing various NMF variants and their interpretations for clustering tasks.

Contribution

It provides a comprehensive overview of NMF methods and their theoretical links to clustering, including recent variants and their applications.

Findings

NMF is closely linked to clustering techniques.

Various NMF variants offer different clustering interpretations.

The review highlights the theoretical foundations connecting NMF and clustering.

Abstract

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.