A Learning Algorithm for the Blind Separation of Non-zero Skewness Source Signals with No Spurious Equilibria

摘要

Neural computational approach to blind sources separation was first introduced by Jutten and Herault [6], and further developed by others [9, 3, 7, 4]. Necessary and sufficient conditions for the blind sources separation have been proposed by Cardoso [1], Tong et al [10, 11], and Common [5]. There have been difficulties of implementing necessary and sufficient conditions by a neural network with no spurious equilibria. In this paper, we present a necessary and sufficient condition for the blind sources separation, which can be implemented by a neural network with no spurious equilibria. Specifically, if the source signals are independent and each of them has a non-zero skewness (3rd-order cumulant), then the sources are separated by a linear transformation, if and only if all the 2nd- and 3rd-order cross-cumulants of the output are zero. This condition does not require the 3rd-order cumulants among three different variables to be zero. Because the condition requires only pairwise statistics (statistics between two different variables), it can be implemented by a neural network with no spurious equilibria.