Non-euclidean independent component analysis and Oja's learning

ESANN 2013 proceedings, 21st European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning

Volumn , Issue , 2013, Pages 125-130

  Lange, M ^a   Biehl, M ^b   Villmann, T ^a  

^a UNIVERSITY OF APPLIED SCIENCES MITTWEIDA   (Germany)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EUCLIDEAN SPACES; INDEPENDENT COMPONENT ANALYSIS(ICA); ISOMORPHIC MAPPING; LINEAR DEMIXING; LINEAR UNMIXING; NON-LINEAR ICA; NONLINEAR INDEPENDENT COMPONENT ANALYSIS; REPRODUCING KERNEL HILBERT SPACES;

BLIND SOURCE SEPARATION; LEARNING ALGORITHMS; LEARNING SYSTEMS; MAPPING; NEURAL NETWORKS;

INDEPENDENT COMPONENT ANALYSIS;

EID: 84887046946     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (29)

1. N. Aronszajn. Theory of reproducing kernels. Transactions of the American Mathematical Society, 68:337-404, 1950.
2. F. Bach and M. Jordan. Kernel independent component analysis. Journal of Machine Learning Research, 3:1-48, 2002.
3. M. Biehl, M. Kästner, M. Lange, and T. Villmann. Non-euclidean principal component analysis and Oja's learning rule _ theoretical aspects. In P. Estevez, J. Principe, and P. Zegers, editors, Advances in Self-Organizing Maps: 9th International Workshop WSOM 2012 Santiage de Chile, volume 198 of Advances in Intelligent Systems and Computing, pages 23-34, Berlin, 2012. Springer.
4. J.-F. Cardoso. Infomax and maximum likelihood for source separation. IEEE Letters on Signal Processing, 4:112-114, 1997.
5. A. Cichocki and S. Amari. Adaptive Blind Signal and Image Processing. John Wiley, 2002.
6. P. Comon and C. Jutten. Handbook of Blind Source Separation. Academic Press, 2010.
7. S. Harmeling, A. Ziehe, and M. K. K.-R. Müller. Kernel-based nonlinear blind source separation. Neural Computation, 15(5):1089-1124, 2003.
8. D. Hebb. The Organization of Behavior. A Neuropsychological Theory. John Wiley, New York, 1949.
9. A. Hyvärinen. The fixed-point algorithm and maximum likelihood estimation for independent component analysis. IEEE Transactions on Neural Networks, 10(3):626-634, 1999.
10. A. Hyvärinen, J. Karhunen, and E. Oja. Independent Component Analysis. J. Wiley & Sons, 2001.
11. A. Hyvärinen and E. Oja. Simple neuron models for independent component analysis. International Journal of Neural Systems, 7(6):671-687, 1996.
12. A. Hyvärinen and E. Oja. Independent component analysis by general nonlinear hebbianlike learning rules. Signal Processing, 64:301-313, 1998.
13. I. Joliffe. Principal Component Analysis. Springer, 2nd edition, 2002.
14. M. Jones and R. Sibson. What is projection pursuit? Journal of the Royal Statistical Society, Series A, 150:1-36, 1987.
15. C. Jutten and J. Hérault. Blind separation of sources, Part I: An adaptive algorithm based on neuromimetic architecture. Signal Processing, 24:1-10, 1991.
16. C. Jutten and J. Karhunen. Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures. International Journal of Neural Systems, 14(5):267-292, 2004.
17. J. Karhunen, E. Oja, L. Wang, R. Vigário, and J. Joutsensalo. A class of neural networks for independnet component analysis. IEEE Transactions on Neural Networks, 8(3):486-504, 1997.
18. J. Karhunen, P. Pajunen, and E. Oja. The nonlinear PCA criterion in blind source separation: Relations with other approaches. Neurocomputing, 22:5-20, 1998.
19. D. Mackay. Information Theory, Inference and Learning Algorithms. Cambridge University Press, 2003.
20. D. Martinez and A. Bray. Nonlinear blind source separation using kernels. IEEE Transactions on Neural Networks, 14(1):228-235, 2003.
21. J. Mercer. Functions of positive and negative type and their connection with the theory of integral equations. Philosophical Transactions of the Royal Society, London, A, 209:415-446, 1909.
22. J.-P. Nadal and N. Parga. Non-linear neurons in the low noise limit: a factorial code maximizes information transfer. Netw, 5:565-581, 1994.
23. E. Oja. Neural networks, principle components and subspaces. International Journal of Neural Systems, 1:61-68, 1989.
24. E. Oja. The nonlinear PCA learning rule in independent component analysis. Neurocomputing, 17:25-45, 1997.
25. D. Pham. Mutual information approach to blind separation of stationary sources. IEEE Transactions on Information Theory, 48:1935-1946, 2002.
26. D.-T. Pham, P. Garat, and C. Jutten. Separation of a mixture of independent sources through a maximum likelihood approach. In J. Vandewalle, R. Boite, M. Moonen, and A. Oosterlinck, editors, Signal Processing VI: Theories and Applications (EUSIPCO), pages 771-774, 1997.
27. B. Schölkopf and A. Smola. Learning with Kernels. MIT Press, 2002.
28. I. Steinwart. On the influence of the kernel on the consistency of support vector machines. Journal of Machine Learning Research, 2:67-93, 2001.
29. T. Villmann and S. Haase. A note on gradient based learning in vector quantization using differentiable kernels for Hilbert and Banach spaces. Machine Learning Reports, 6(MLR-02-2012):1-29, 2012. ISSN:1865-3960, http://www.techfak.uni-bielefeld.de/ ~fschleif/mlr/mlr_02_2012.pdf.