Discriminative Non-negative Matrix Factorization for Multiple Pitch Estimation

In this paper, we present a supervised method to improve the multiple pitch estimation accuracy of the non-negative matrix factorization (NMF) algorithm. The idea is to extend the sparse NMF framework by incorporating pitch information present in time-aligned musical scores in order to extract features that enforce the separability between pitch labels. We introduce two discriminative criteria that maximize inter-class scatter and quantify the predictive potential of a given decomposition using logistic regressors. Those criteria are applied to both the latent variable and the deterministic autoencoder views of NMF, and we devise efficient update rules for each. We evaluate our method on three polyphonic datasets of piano recordings and orchestral instrument mixes. Both models greatly enhance the quality of the basis spectra learned by NMF and the accuracy of multiple pitch estimation.