Equi-convergence algorithm for blind separation of sources with arbitrary distributions

Abstract

This paper presents practical implementation of the equi- convergent learning algorithm for blind source separation. The equi- convergent algorithm [4] has favorite properties such as isotropic con-vergence and universal convergence, but it requires to estimate unknown activation functions and certain unknown statistics of source signals. The estimation of such activation functions and statistics becomes critical in realizing the equi-convergent algorithm. It is the purpose of this paper to develop a new approach to estimate the activation functions adaptively for blind source separation. We propose the exponential type family as a model for probability density functions. A method of constructing an exponential family from the activation ( score ) functions is proposed. Then, a learning rule based on the maximum likelihood is derived to update the parameters in the exponential family. The learning rule is compatible with minimization of mutual information for training deinix- ing models. Finally, computer simulations are given to demonstrate the effectiveness and validity of the proposed approach. © Springer-Verlag Berlin Heidelberg 2001.