Hierarchical and coupled non-negative dynamical systems with application to audio modeling

Many kinds of non-negative data, such as power spectra and count data, have been modeled using non-negative matrix factorization. Even though this modeling paradigm has yielded successful applications, it falls short when the data have certain hierarchical and temporal structure. In this study, we propose a novel dynamical system model that can handle these kinds of complex structures that often arise in non-negative data. We show that our model can be extended to handle heterogeneous data for data-driven regularization. We present convergence-guaranteed update rules for each latent factor. In order to assess the performance, we evaluate our model on the transcription of classical piano pieces, and show that it outperforms related models. We also illustrate that the performance can be further improved by making use of symbolic data.