Joint Approximate Diagonalization Using Bilateral Rank-Reducing Householder Transform with Application in Blind Source Separation

This paper addresses the problem of Joint approximate diagonalization (JAD) of a set of given matrices and proposes a new efficient iterative algorithm for JAD that based on the rank-reducing structure of Householder transform. The proposed algorithm, named as HJD, completes the simultaneous diagonalization of the target matrices by successive Householder transform from the point of view of matrix power concentration. Generally, the power of the elements below diagonal element was concentrated to the diagonal element by the rank-reducing Householder transform. Such a particular structure of Householder transform at each iteration prevents the divergence of matrix power. The diagonalization matrix was calculated by the product of all Householder matrices. By applying our algorithm to blind source separation, we demonstrate the efficiency and improvement of the proposed algorithm in estimating the separation matrix.