Stability and chaos analysis for an ICA algorithm

Authors:
Min Wan;Zhang Yi;Jian Cheng Lv;Jiliu Zhou
Affiliations:
Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, PR China;Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu, 610065, PR China;Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu, 610065, PR China;Machine Intelligence Laboratory, College of Computer Science, Sichuan University, Chengdu, 610065, PR China
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 7
Cited 0

Independent component analysis, a new concept?

Signal Processing - Special issue on higher order statistics
On-line Algorithm for Blind Signal Extraction of Arbitrarily Distributed, but Temporally Correlated Sources Using Second Order Statistics

Neural Processing Letters
Stability and Chaos of a Class of Learning Algorithms for ICA Neural Networks

Neural Processing Letters
Dynamic behavior of a discrete modified Ricker & Beverton-Holt model

Computers & Mathematics with Applications
Convergence analysis of a class of Hyvärinen-Oja's ICA learning algorithms with constant learning rates

IEEE Transactions on Signal Processing
On the discrete-time dynamics of the basic Hebbian neural network node

IEEE Transactions on Neural Networks
Convergence analysis of a deterministic discrete time system of Oja's PCA learning algorithm

IEEE Transactions on Neural Networks

Quantified Score

Hi-index	0.09

Visualization

Abstract

The stability and chaos of an ICA algorithm are investigated by analyzing the corresponding deterministic discrete time (DDT) system. The existence and stability of all the possible fixed points of the ICA algorithm are studied. While the nonlinear function contained in the algorithm is specified, an invariant set of the algorithm is obtained so that the non-divergence of the algorithm can be guaranteed. It is then derived in this invariant set that the behaviors of the algorithm are dominated by a one-dimensional map. The conditions for convergence and chaos are derived. In the outside of the invariant set, the corrected Marotto's theorem and computer-assisted method are applied to study the two-dimensional case of the algorithm and the existence of chaos is proved. The attractors and bifurcation diagrams of the algorithm with different parameters are presented to further confirm the obtained results.