A fast approximate joint diagonalization algorithm using a criterion with a block diagonal weight matrix

Abstract

We propose a new algorithm for Approximate Joint Diagonalization (AJD) with two main advantages over existing state-of-the-art algorithms: Improved overall running speed, especially in large-scale (high-dimensional) problems; and an ability to incorporate specially structured weight-matrices into the AJD criterion. The algorithm is based on approximate Gauss iterations for successive reduction of a weighted Least Squares off-diagonality criterion. The proposed Matlab® implementation allows AJD of ten 100 × 100 matrices in 3–4 seconds (for the unweighted case) on a common PC (Pentium M, 1.86GHz, 2GB RAM), generally 3–5 times faster than the fastest competitor. The ability to incorporate weights allows fast large-scale realization of optimized versions of classical blind source separation algorithms, such as Second-Order Blind Identification (SOBI), whose weighted version (WASOBI) yields significantly improved separation performance.