Stability analysis of learning algorithms for blind source separation

Recently a number of adaptive learning algorithms have been proposed for blind source separation. Although the underlying principals and approaches are different, most of them have very similar forms. Two important issues remained to be elucidated further: the statistical efficiency and the stability of learning algorithms. The present letter analyzes a general form of statistically efficient algorithms and gives a necessary and sufficient condition for the separating solution to be a stable equilibrium of a general learning algorithm. Moreover, when the separating solution is unstable, a simple method is given for stabilizing the separating solution by modifying the algorithm. (C) 1997 Elsevier Science Ltd.