Sparse nonnegative matrix factorization with l0-constraints

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the l(1)-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the l(0)-pseudo-norm. In this paper, we propose a framework for approximate NMF which constrains the l(0)-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches. (C) 2011 Elsevier B.V. All rights reserved.