Stability Analysis of Learning Algorithms for Blind Source Separation

• Published in: Neural networks Vol. 10; no. 8; pp. 1345 - 1351
• Main Authors: Amari, Shun-ichi, Chen, Tian-ping, Cichocki, Andrzej
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.11.1997; Elsevier Science
• Subjects: Applied sciences; Artificial intelligence; Blind source separation; Computer science; control theory; systems; Connectionism. Neural networks; Efficiency of learning; Exact sciences and technology; Independent component analysis (ICA); Natural gradient; Stability of learning; Stability of learning; Blind source separation; Efficiency of learning; Natural gradient; Independent component analysis (ICA); Learning; Stability; Adaptive algorithm; Necessary and sufficient condition; Signal estimation; Neural network; Asymptotic convergence
• ISSN: 0893-6080; 1879-2782; 1879-2782
• DOI: 10.1016/S0893-6080(97)00039-7

Recently a number of adaptive learning algorithms have been proposed for blind source separation. Although the underlying principles 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.