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 Formula: see text of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the Formula: see text. In this paper, we propose a framework for approximate NMF which constrains the Formula: see text 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.