Majorization-minimization for Sparse Nonnegative Matrix Factorization with the $\beta$-divergence

arXiv:2207.06316v4 Announce Type: replace
Abstract: This article introduces new multiplicative updates for nonnegative matrix factorization with the $\beta$-divergence and sparse regularization of one of the two factors (say, the activation matrix). It is well known that the norm of the other factor (the dictionary matrix) needs to be controlled in order to avoid an ill-posed formulation. Standard practice consists in constraining the columns of the dictionary to have unit norm, which leads to a nontrivial optimization problem. Our approach leverages …

abstract article arxiv beta cs.lg dictionary divergence factorization math.oc matrix norm regularization type updates