Dynamic non-negative models for audio source separation

As seen so far, non-negative models can be quite powerful when it comes to resolving mixtures of sounds. However, in such models we often ignore temporal information, instead focusing on resolving each incoming spectrum independently. In this chapter we will present some methods that learn to incorporate the temporal aspects of sounds and use that information to perform improved separation. We will show three such models, a conlvolutive model that learns fixed temporal features, a hidden Markov model that learns state transitions and can incorporate language information, and finally a continuous dynamical model that learns how sounds evolve over time and is able to resolve cases where static information is not enough.