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

摘要

The design and adjustment of the divergence in audio applicationsusing nonnegative matrix factorization (NMF) is still open problem.In this study, to deal with this problem, we explore a representation of thedivergence using neural networks (NNs). Instead of the divergence, ourapproach extends the multiplicative update algorithm (MUA), which estimatesthe NMF parameters, using NNs. The design of the extended MUAincorporates NNs, and the new algorithm is referred to as the deep MUA(DeMUA) for NMF. While the DeMUA represents the algorithm for theNMF, interestingly, the divergence is obtained from the incorporated NN.In addition, we propose theoretical guides to design the incorporated NNsuch that it can be interpreted as a divergence. By appropriately designingthe NN, MUAs based on existing divergences with a single hyper-parametercan be represented by the DeMUA. To train the DeMUA, we applied it toaudio denoising and supervised signal separation. Our experimental resultsshow that the proposed architecture can learn the MUA and the divergencesin sparse denoising and speech separation tasks and that the MUA based ongeneralized divergences with multiple parameters shows favorable performanceson these tasks.