Deep Multiplicative Update Algorithm for Nonnegative Matrix Factorization and Its Application to Audio Signals

The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.