Sparse nonnegative matrix factorization using ℓ0-constraints

Although nonnegative matrix factorization (NMF) favors a part-based and sparse representation of its input, there is no guarantee for this behavior. Several extensions to NMF have been proposed in order to introduce sparseness via the ℓ
¹
-norm, while little work is done using the more natural sparseness measure, the ℓ
⁰
-pseudo-norm. In this work we propose two NMF algorithms with ℓ
⁰
-sparseness constraints on the bases and the coefficient matrices, respectively. We show that classic NMF is a suited tool for ℓ
⁰
-sparse NMF algorithms, due to a property we call sparseness maintenance. We apply our algorithms to synthetic and real-world data and compare our results to sparse NMF and nonnegative K-SVD.