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

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^reg implementation allows AJD of ten 100 times 100 matrices in 3-4 seconds (for the unweighted case) on a common PC (Pentium M, 1.86 GHz, 2 GB 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 (WA- SOBI) yields significantly improved separation performance.