Relative group sparsity for non-negative matrix factorization with application to on-the-fly audio source separation

We consider dictionary-based signal decompositions with group sparsity, a variant of structured sparsity. We point out that the group sparsity-inducing constraint alone may not be sufficient in some cases when we know that some bigger groups or so-called supergroups cannot vanish completely. To deal with this problem we introduce the notion of relative group sparsity preventing the supergroups from vanishing. In this paper we formulate practical criteria and algorithms for relative group sparsity as applied to non-negative matrix factorization and investigate its potential benefit within the on-the-fly audio source separation framework we recently introduced. Experimental evaluation shows that the proposed relative group sparsity leads to performance improvement over group sparsity in both supervised and semi-supervised on-the-fly audio source separation settings.