Investigation And Comparison of Optimization Methods for Variational Autoencoder-Based Underdetermined Multichannel Source Separation

In this paper, we investigate two algorithms for variational autoencoder (VAE)-based underdetermined multichannel source separation. We previously extended the multichannel VAE (MVAE) method for determined multichannel source separation and proposed the generalized MVAE (GMVAE) method for underdetermined multichannel source separation. The GMVAE method employs a conditional VAE (CVAE) as the source model representing the power spectrograms of the underlying sources present in a mixture. While we developed a convergence-guaranteed parameter estimation algorithm using a majorization-minimization/minorization-maximization (MM) algorithm, an expectation-maximization (EM) algorithm also allows us to design another algorithm with the same property. However, a comparison of the MM-based and EM-based algorithms has not yet been revealed. To elucidate this, we investigate the MM-based and EM-based algorithms for the GMVAE method, using an improved CVAE variant called auxiliary classifier VAE (ACVAE). The experimental results suggest that the EM-based algorithm takes less computational cost, achieving comparable separation performance with the MM-based algorithm.