Non-negative matrix factorization with sparseness constraints

TL;DR

This paper enhances non-negative matrix factorization by incorporating sparseness constraints, leading to more interpretable parts-based representations, and provides MATLAB implementations to facilitate broader application in data analysis.

Contribution

It introduces a sparseness constraint extension to NMF, improving the quality of parts-based decompositions and offers MATLAB code for practical use.

Findings

Sparseness constraints improve interpretability of NMF results.

The extended NMF produces more localized and meaningful parts.

MATLAB code availability promotes wider adoption.

Abstract

Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in parts-based representations. In this paper, we show how explicitly incorporating the notion of `sparseness' improves the found decompositions. Additionally, we provide complete MATLAB code both for standard NMF and for our extension. Our hope is that this will further the application of these methods to solving novel data-analysis problems.