Non-orthogonal approximate joint diagonalization of non-Hermitian matrices in the least-squares sense

摘要

A non-orthogonal approximate joint diagonalization (AJD) algorithm of a set of non-Hermitian matrices is presented. Specifically, the proposed algorithm aims to find two distinct general (not necessarily orthogonal nor square) diagonalizing matrices which minimize the least-squares (LS) criterion based on the gradient and an optimal rank-1 approximation approach. It can be used to compute the canonical polyadic decomposition (CPD) of the third-order tensor. Simulation results demonstrate that the proposed algorithm has good convergence, robustness and accuracy properties. The joint blind source separation UBSS) problem of two datasets can be effectively solved based on the proposed algorithm. (C) 2019 Elsevier B.V. All rights reserved.