Introduction to Nonnegative Matrix Factorization

TL;DR

This paper provides an overview of nonnegative matrix factorization (NMF), discussing its applications, mathematical properties, algorithms, and its relation to other low-rank approximation problems.

Contribution

It offers a concise introduction to NMF, covering its theoretical foundations, practical applications, and connections to broader matrix approximation problems.

Findings

NMF is applicable in hyperspectral imaging.

Discussion of the geometry and uniqueness of NMF solutions.

Analysis of algorithms and complexity for NMF.

Abstract

In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions, complexity, algorithms, and its link with extended formulations of polyhedra. In order to put NMF into perspective, the more general problem class of constrained low-rank matrix approximation problems is first briefly introduced.