On the clustering aspect of nonnegative matrix factorization

TL;DR

This paper offers a theoretical explanation for why nonnegative matrix factorization (NMF) effectively produces clustering results, even without orthogonality or sparsity constraints, supporting its use as a clustering method.

Contribution

It proves that standard NMF can yield clustering results without additional constraints, providing theoretical backing for its effectiveness in clustering tasks.

Findings

NMF can produce clustering results without orthogonality or sparsity constraints

Theoretical support for NMF's superiority in clustering

Validates previous empirical observations about NMF's clustering ability

Abstract

This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still can give clustering results, thus providing a theoretical support for many works, e.g., Xu et al. [1] and Kim et al. [2], that show the superiority of the standard NMF as a clustering method.