Fast adaptive eigenvalue decomposition: a maximum likelihood approach

In this paper, we address the problem of adaptive eigenvalue decomposition (EVD). We propose a new approach, based on the optimization of the log-likelihood criterion. The parameters of the log-likelihood to be estimated are the eigenvectors and the eigenvalues of the data covariance matrix. They are actualized by means of a stochastic algorithm that requires little computational cost. Furthermore, the particular structure of the algorithm, that we named MALASE, ensures the orthonormality of the estimated basis of eigenvectors at each step of the algorithm. MALASE algorithm shows strong links with many Givens rotation based update algorithms that we discuss. We consider convergence issues for MALASE algorithm and give the expression of the asymptotic covariance matrix of the estimated parameters. The practical interest of the proposed method is shown on examples. ? 2002 Elsevier Science B.V. All rights reserved.