The convergence analysis of the complex ICA algorithms using symmetric orthogonalization

The contrast function optimization based independent component analysis is one of the most widespread methods in separating independent sources from their linear mixtures. The convergence analysis of such algorithms, which has both theoretical and practical value, is a current research focus. In this article, we present a convergence analysis for the separation of complex sources via use of these algorithms. Based on this analysis, we provide the characterization of the stationary points of the algorithms using symmetric orthogonalization.

[1]  Constantinos B. Papadias,et al.  Globally convergent blind source separation based on a multiuser kurtosis maximization criterion , 2000, IEEE Trans. Signal Process..

[2]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[3]  Hualiang Li,et al.  Gradient and Fixed-Point Complex ICA Algorithms Based on Kurtosis Maximization , 2006, 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing.

[4]  Phillip A. Regalia,et al.  Monotonic convergence of fixed-point algorithms for ICA , 2003, IEEE Trans. Neural Networks.

[5]  Alper T. Erdogan,et al.  On the Convergence of ICA Algorithms With Symmetric Orthogonalization , 2008, IEEE Transactions on Signal Processing.

[6]  A. Bos Complex gradient and Hessian , 1994 .

[7]  E. Oja,et al.  Convergence of the symmetrical FastICA algorithm , 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

[8]  Ken Kreutz-Delgado,et al.  The Complex Gradient Operator and the CR-Calculus ECE275A - Lecture Supplement - Fall 2005 , 2009, 0906.4835.

[9]  Dimitri P. Bertsekas,et al.  Convex Analysis and Optimization , 2003 .

[10]  Are Hjørungnes,et al.  Complex-Valued Matrix Differentiation: Techniques and Key Results , 2007, IEEE Transactions on Signal Processing.