Non-negative Matrix Factorization with Sparseness Constraints

TLDR

Non‑negative matrix factorization (NMF) is a technique for parts‑based linear representations of non‑negative data, though it does not always produce such representations. The authors aim to demonstrate that enforcing sparseness in NMF yields improved decompositions and to encourage its use in new data‑analysis tasks. They extend NMF by explicitly imposing sparseness constraints and supply MATLAB code for both the standard and the extended algorithms.

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.