Supervised nonnegative matrix factorization with Dual-Itakura-Saito and Kullback-Leibler divergences for music transcription

In this paper, we present a convex-analytic approach to supervised nonnegative matrix factorization (SNMF) based on the Dual-Itakura-Saito (Dual-IS) and Kullback-Leibler (KL) divergences for music transcription. The Dual-IS and KL divergences define convex fidelity functions, whereas the IS divergence defines a nonconvex one. The SNMF problem is formulated as minimizing the divergence-based fidelity function penalized by the ℓ₁ and row-block ℓ₁ norms subject to the nonnegativity constraint. Simulation results show that (i) the use of the Dual-IS and KL divergences yields better performance than the squared Euclidean distance and that (ii) the use of the Dual-IS divergence prevents from false alarms efficiently.