Sparse nonnegative matrix factorization with ℓ(0)-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.