@ARTICLE{ZieLasNolMue04,
    author = {Ziehe, Andreas and Laskov, Pavel and Nolte, Guido and M\"uller, Klaus-Robert},
    title = "A Fast Algorithm for Joint Diagonalization with Non-orthogonal Transformations and its Application to Blind Source Separation",
    journal = "Journal of Machine Learning Research",
    year = "2004",
    volume = "5",
    pages = "777-800",
    month = "Jul",
    abstract = "A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non-orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems.",
    pdf = "http://www.jmlr.org/papers/volume5/ziehe04a/ziehe04a.pdf"
}