Analysis of the convergence properties of self-normalized source separation neural networks

An extended source separation neural network was derived by Cichocki et al. (see Proc. 1995 Int. Symp. Nonlinear Theory Appl. NOLTA, Las Vegas, NV, p.61-65, 1995) from the classical Herault-Jutten network. It claimed to have several advantages, but its convergence properties were not described. In this paper, we first consider the standard version of this network. We determine all its equilibrium points and analyze their stability for a small adaptation gain. We prove that the stationary independent sources that this network can separate are the globally sub-Gaussian signals. As the Herault-Jutten (1991) network applies to the same sources, we thus show that the advantages of the new network are not counterbalanced by a reduced field of application, which confirms its attractiveness in the considered conditions. Moreover, we then introduce and analyze a modified version of this network, which can separate the globally super-Gaussian source signals. These theoretical results are experimentally confirmed by computer simulations. As a result of our overall investigation, a method for processing each one of the two classes of signals (i.e. sub- and super-Gaussian) is available