Learning the Statistical Model of the NMF Using the Deep Multiplicative Update Algorithm with Applications

Nonnegative matrix factorization (NMF) is widely used in the audio applications. In these applications, recently, the cost functions based on the complex probability distribution and the optimization algorithms have been developed. However, the flexibility of these methods is limited because the cost functions have only one or no hyper-parameter. Thus, in this paper, we utilize a neural network to construct a generalized cost function of the NMF. Moreover, we propose a novel neural network architecture to estimate the NMF parameters. The proposed neural network solves the NMF optimization problem of which cost function is parameterized by the part of itself. We show the proposed neural network can learn a statistical model by applying it to the denoising and the signal separation tasks.