Jacobi-like nonnegative joint diagonalization by congruence

A new joint diagonalization by congruence algorithm is presented, which allows the computation of a nonnegative joint diagonalizer. The nonnegativity constraint is ensured by means of a square change of variable. Then we propose a Jacobi-like approach using LU matrix factorization, which consists of formulating a high-dimensional optimization problem into several sequential one-dimensional subproblems. Numerical experiments emphasize the advantages of the proposed method, especially in the presence of bottlenecks such as for low SNR values and a small number of available matrices. An illustration of blind source separation shows the interest of the proposed algorithm.