Second order Hebbian neural networks and blind source separation

The adaptive blind source separation problem has been traditionally dealt with the use of nonlinear neural models implementing higher-order statistical methods. In this paper we show that second order Cross-Coupled Hebbian rule used for Asymmetric Principal Component Analysis (APCA) is capable of blindly and adaptively separating uncorrelated sources. Our method enjoys the following advantages over similar higher-order models such as those performing Independent Component Analysis (ICA): (a) the strong independence assumption about the source signals is reduced to the weaker uncorrelation assumption, (b) there is no constraint on the sources pdf's, i.e. we remove the assumption that at most one signal is Gaussian, and (c) the higher order statistical optimization methods are replaced with second order methods with no local minima, and(d) the kurtosis of the sources becomes irrelevant. Simulation experiments shows that the model successfully separates source images with kurtoses of different signs.