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

Authors:
Jian Cheng Lv;Kok Kiong Tan;Zhang Yi;Sunan Huang
Affiliations:
Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore 117576;Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore 117576;Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, People's Republic of China 610054;Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore 117576
Venue:
Neural Processing Letters
Year:
2008

Citing 17
Cited 2

Blind separation of sources, Part 1: an adaptive algorithm based on neuromimetic architecture

Signal Processing
Modified Hebbian learning for curve and surface fitting

Neural Networks
Independent component analysis, a new concept?

Signal Processing - Special issue on higher order statistics
Independent component analysis by general nonlinear Hebbian-like learning rules

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

Neural Processing Letters
Applications of Neural Blind Separation to Signal and Image Processing

ICASSP '97 Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97) -Volume 1 - Volume 1
Convergence Analysis of Recurrent Neural Networks (Network Theory and Applications, V. 13)

Convergence Analysis of Recurrent Neural Networks (Network Theory and Applications, V. 13)
Feature Extraction Using Independent Components of Each Category

Neural Processing Letters
On the Effect of the Form of the Posterior Approximation in Variational Learning of ICA Models

Neural Processing Letters
A Resampling Test for the Total Independence of Stationary Time Series: Application to the Performance Evaluation of ICA Algorithms

Neural Processing Letters
Global convergence of Oja's PCA learning algorithm with a non-zero-approaching adaptive learning rate

Theoretical Computer Science
Robust Prewhitening for ICA by Minimizing β-Divergence and Its Application to FastICA

Neural Processing Letters
A class of neural networks for independent component analysis

IEEE Transactions on Neural Networks
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
The FastICA Algorithm Revisited: Convergence Analysis

IEEE Transactions on Neural Networks
Global Convergence of GHA Learning Algorithm With Nonzero-Approaching Adaptive Learning Rates

IEEE Transactions on Neural Networks

Stability and chaos analysis for an ICA algorithm

Computers & Mathematics with Applications
Multistability of α-divergence based NMF algorithms

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Independent component analysis (ICA) neural networks can estimate independent components from the mixed signal. The dynamical behavior of the learning algorithms for ICA neural networks is crucial to effectively apply these networks to practical applications. The paper presents the stability and chaotic dynamical behavior of a class of ICA learning algorithms with constant learning rates. Some invariant sets are obtained so that the non-divergence of these algorithms can be guaranteed. In these invariant sets, the stability and chaotic behaviors are analyzed. The conditions for stability and chaos are derived. Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior.