Discriminative separable nonnegative matrix factorization by structured sparse regularization

Non-negative matrix factorization (NMF) is one of the most important models for learning compact representations of high-dimensional data. With the separability condition, separable NMF further enjoys a global optimal solution. However, separable NMF is unable to make use of data label information and thus unfavourable for supervised learning problems. In this paper, we propose discriminative separable NMF (DS-NMF), which extends separable NMF by encoding data label information into data representations. Assuming that each conical basis vector under the separability condition is only contributable to representing data from a few classes, DS-NMF exploits a structured sparse regularization to learning a sparse data representation and provides higher discrimination power than the standard separable NMF. Empirical evaluations on face recognition and scene classification problems confirm the effectiveness of DS-NMF and its superiority to separable NMF.