Abstract
We propose Blind Source Separation (BSS) techniques that are applicable to a wide class of source distributions that may be skewed or symmetric and may even have zero kurtosis. Skewed distributions are encountered in many important application areas such as communications and biomedical signal processing. The methods stem from maximum likelihood approach. Powerful parametric models based on the Extended Generalized Lambda Distribution (EGLD) and the Pearson system are employed in finding the score function. Model parameters are adaptively estimated using conventional moments or linear combinations of order statistics (L-moments). The developed methods are compared with the existing methods quantitatively. Simulation examples demonstrate the good performance of the proposed methods in the cases where the standard Independent Component Analysis (ICA) methods perform poorly.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Choi, A. Cichocki, and S. Amari, “Flexible Independent Component Analysis,” in Neural Networks for Signal Processing VIII, 1998, Proceedings of the 1998 IEEE Signal Processing Society Workshop, 1998, pp. 83-92.
J. Cao and N. Murata, “A Stable and Robust ICA Algorithm Based on t-distribution and Generalized Gaussian Distribution Models,” in Neural Networks for Signal Processing IX, 1999, The IEEE 1999 Proceedings, 1999, pp. 283-292.
A. Hyvärinen, “Fast and Robust Fixed-Point Algorithms for Independent Component Analysis,” IEEE Transactions on Neural Networks, vol. 10,no. 3, 1999, pp. 626-634.
J.F. Cardoso, “Blind Signal Separation: Statistical Principles,” Proceedings of the IEEE, vol. 86,no. 10, 1998, pp. 2009-2025.
J.F. Cardoso, “Infomax and Maximum Likelihood for Blind Signal Processing,” IEEE Signal Processing Letters, vol. 4,no. 4, 1997.
T.-W. Lee, Independent Component Analysis: Theory and applications, Boston: Kluwer Academic Publishers, 1998.
S.-I. Amari and A. Cichocki, “Adaptive Blind Signal Processing—Neural Network Approaches,” Proceedings of the IEEE, vol. 86,no. 10, 1998, pp. 2026-2048.
D.T. Pham, “Blind Separation of Instantaneous Mixture of Sources via an Independent Component Analysis,” IEEE Transactions on Signal Processing, vol. 44,no. 11, 1996, pp. 2768-2779.
J. Eriksson, J. Karvanen, and V. Koivunen, “Source Distribution Adaptive Maximum Likelihood Estimation of ICA Model,” in ICA2000, Proceedings of the Second International Workshop on Independent Component Analysis and Blind Signal Separation, 2000, pp. 227-232.
J. Karvanen, J. Eriksson, and V. Koivunen, “Pearson System Based Method for Blind Separation,” in ICA2000, Proceedings of the Second International Workshop on Independent Component Analysis and Blind Signal Separation, 2000, pp. 585-590.
Z.A. Karian, E.J. Dudewicz, and P. McDonald, “The Extended Generalized Lambda Distribution System for Fitting Distributions to Data: History, Completion of Theory, Tables, Applications, the “Final Word” on Moment Fits,” Communications in Statistics: Simulation and Computation, vol. 25,no. 3, 1996, pp. 611-642.
A. Stuart and J.K. Ord, Kendall's Advanced Theory of Statistics: Distribution Theory, vol. 1, 6th edn., London: Edward Arnold, 1994.
J. Hosking, “L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics,” Journal of Royal Statistical Society B, vol. 52,no. 1, 1990, pp. 105-124.
Z.A. Karian and E.J. Dudewicz, “The Extended Generalized Lambda Distribution (EGLD) System for Fitting Distributions to Data with Moments, II: Tables,” American Journal of Mathematical and Management Sciences, 1996.
J. Eriksson, J. Karvanen, and V. Koivunen, EGLD-ICA Matlab Code Available at http://wooster.hut.fi/statsp/publications.html, 2000.
S.-I. Amari, “Natural Gradient Works Efficiently in Learning,” Neural Computation, vol. 10, 1998, pp. 251-276.
A. Hyvärinen, “The Fixed-Point Algorithm and Maximum Likelihood Estimation for Independent Component Analysis,” Neural Processing Letters, vol. 10,no. 1, 1999, pp. 1-5.
J. Karvanen, J. Eriksson, and V. Koivunen, Pearson-ICA Matlab Code Available at http://wooster.hut.fi/statsp/publications.html, 2000.
G.W. Steward and J.-G. Sun, Matrix Perturbation Theory, Boston: Academic Press, 1990.
S.-I. Amari, A. Cichocki, and H. Yang, “A New Learning Algorithm for Blind Signal Separation,” in Advances in Neural Information Processing Systems, vol. 8, Cambridge MA: MIT Press, 1996, pp. 757-763.
J.F. Cardoso, JADE Matlab Code with References Available at http://sig.enst.fr:80/~cardoso/.
T.-W. Lee, M. Girolami, and T. Sejnowski, Infomax Matlab Code with References Available at http://www.cnl.salk.edu/~scott/ica-download-form.html.
A. Hyvärinen, FastICA Matlab Code with References Available at http://www.cis.hut.fi/projects/ica/fastica/, 1998.
S. Cruces, L. Castedo, and A. Cichocki, “Novel Blind Source Separation Algorithms Using Cumulants,” in Proc. of ICASSP, 2000, pp. 3152-3155.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Karvanen, J., Eriksson, J. & Koivunen, V. Adaptive Score Functions for Maximum Likelihood ICA. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 32, 83–92 (2002). https://doi.org/10.1023/A:1016367418778
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1016367418778