Adaptive Group Sparsity for Non-Negative Matrix Factorization with Application to Unsupervised Source Separation

Abstract

Non-negative matrix factorization (NMF) is an appealing technique for many audio applications, such as automatic music transcription, source separation and speech enhancement. Sparsity constraints are commonly used on the NMF model to discover a small number of dominant patterns. Recently, group sparsity has been proposed for NMF based methods, in which basis vectors belonging to a same group are permitted to activate together, while activations across groups are suppressed. However, most group sparsity models penalize all groups using a same parameter without considering the relative importance of different groups for modeling the input data. In this paper, we propose adaptive group sparsity to model the relative importance of different groups with adaptive penalty parameters and investigate its potential benefit to separate speech from other sound sources. Experimental results show that the proposed adaptive group sparsity improves the performance over regular group sparsity in unsupervised settings where neither the speaker identity nor the type of noise is known in advance.