Entropy optimization by the PFANN network: application to blind source separation

Abstract

The aim of this paper is to present a study of polynomial functional-link neural units that learn through an information-theoretic-based criterion. First the structure of the neuron is presented and the unsupervised learning theory is explained and discussed, with particular attention being paid to its probability density function and cumulative distribution function approximation capability. Then a neural network formed by such neurons (the polynomial functional-link artificial neural network, or PFANN) is shown to be able to separate out linearly mixed eterokurtic source signals, i.e. signals endowed with either positive or negative kurtoses. In order to compare the performance of the proposed blind separation technique with those exhibited by existing methods, the mixture of densities (MOD) approach of Xu et al, which is closely related to PFANN, is briefly recalled; then comparative numerical simulations performed on both synthetic and real-world signals and a complexity evaluation are illustrated. These results show that the PFANN approach gives similar performance with a noticeable reduction in computational effort.