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 l1-norm of the factor matrices, while little work has been done using a more natural sparseness measure, the l0-pseudo-norm. In the paper “Sparse nonnegative matrix factorization with l0-constraints”, we propose a framework for approximate NMF which constrains the l0-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. This package contains Matlab implementations of our algorithms and experimental setups to reproduce our results.

“Sparse nonnegative matrix factorization with l0-constraints”, Robert Peharz and Franz Pernkopf, Neurocomputing, vol. 80, Special Issue on Machine Learning for Signal Processing 2010, pp. 38-46, 2012.