Stability Analysis of Adaptive Blind Source Separation

Recently a number of adaptive learning algorithms have been proposed for blind source separation. Although the underlying principles and approaches are di erent, most of them have very similar forms. Two important issues have remained to be elucidated further: the statistical e ciency and the stability of learning algorithms. The present letter analyzes a general form of statistically e cient algorithm and give a necessary and su cient 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.