Similarity induced group sparsity for non-negative matrix factorisation

Non-negative matrix factorisations are used in several branches of signal processing and data analysis for separation and classification. Sparsity constraints are commonly set on the model to promote discovery of a small number of dominant patterns. In group sparse models, atoms considered to belong to a consistent group are permitted to activate together, while activations across groups are suppressed, reducing the number of simultaneously active sources or other structures. Whereas most group sparse models require explicit division of atoms into separate groups without addressing their mutual relations, we propose a constraint that permits dynamic relationships between atoms or groups, based on any defined distance measure. The resulting solutions promote approximation with components considered similar to each other. Evaluation results are shown for speech enhancement and noise robust speech and speaker recognition.