Faster independent low-rank matrix analysis with pairwise updates of demixing vectors

Abstract

In this paper, we present an algorithm for independent low-rank matrix analysis (ILRMA) of three or more sources that is faster than that for conventional ILRMA. In conventional ILRMA, demixing vectors are updated one by one by the iterative projection (IP) method. The update rules of IP are derived from a system of quadratic equations obtained by differentiating the objective function of ILRMA with respect to demixing vectors. This system of quadratic equations is called hybrid exact-approximate joint diagonalization (HEAD) and no closed-form solution is known yet for three or more sources. Recently, a method that can update two demixing vectors simultaneously has been proposed for independent vector analysis. The method is derived by reducing HEAD for two sources to a generalized eigenvalue problem and solving the problem. Furthermore, the pairwise updates have recently been extended to the case of three or more sources. However, the efficacy of the pairwise updates for ILRMA has not yet been investigated. Therefore, in this work, we apply the pairwise updates of demixing vectors to ILRMA. By replacing the update rules of demixing vectors with the proposed pairwise updates, we accelerate the convergence of ILRMA. The experimental results show that the proposed method yields faster convergence and better performance than conventional ILRMA.