Kernel-based topographic map formation achieved with an information-theoretic approach

Neural Networks

Volumn 15, Issue 8-9, 2002, Pages 1029-1039

  Van Hulle, Marc M ^a  

^a KU LEUVEN UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Incomplete gamma distribution kernel; Information based learning; Joint entropy maximization; Kernel based topographic maps; Self organizing maps

Indexed keywords

ALGORITHMS; ENTROPY; MAPS; OPTIMIZATION;

TOPOGRAPHIC MAP FORMATION;

NEURAL NETWORKS;

ALGORITHM; ARTIFICIAL NEURAL NETWORK; CONFERENCE PAPER; ENTROPY; LEARNING; PERFORMANCE; PRIORITY JOURNAL;

ALGORITHMS; INFORMATION THEORY; NEURAL NETWORKS (COMPUTER);

EID: 0036791873     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(02)00077-1     Document Type: Conference Paper

References (25)

1. Amari S.-I., Cichocki A., Yang H. A new learning algorithm for blind signal separation. Touretzky D.S., Mozer M., Hasselmo M., Advances in neural processing systems. Vol. 8:1996;757-763 MIT Press, Cambridge, MA.
2. András P. Kernel-Kohonen networks. International Journal of Neural Systems. 12:(2):2001;117-136.
3. Bell A.J., Sejnowski T.J. An information-maximization approach to blind separation and blind deconvolution. Neural Computation. 7:1995;1129-1159.
4. Benaim, M., & Tomasini, L. (1991). Competitive and self-organizing algorithms based on the minimization of an information criterion. Proceedings of the ICANN'91 (pp. 391-396).
5. Bishop C.M., Svensén M., Williams C.K.I. GTM: The generative topographic mapping. Neural Computation. 10:1998;215-234.
6. Cardoso J.-F., Laheld B. Equivariant adaptive source separation. IEEE Transactions on Signal Processing. 44:(12):1996;3017-3030.
7. Durbin R., Willshaw D. An analogue approach to the travelling salesman problem using an elastic net method. Nature. 326:1987;689-691.
8. Graepel T., Burger M., Obermayer K. Phase transitions in stochastic self-organizing maps. Physical Review E. 56:(4):1997;3876-3890.
9. Graepel T., Burger M., Obermayer K. Self-organizing maps: Generalizations and new optimization techniques. Neurocomputing. 21:1998;173-190.
10. Graham R.L., Knuth D.E., Patashnik O. Answer to problem 9.60 in concrete mathematics: A foundation for computer science. 1994;Addison-Wesley, Reading, MA.
11. Kohonen T. Self-organized formation of topologically correct feature maps. Biological Cybernetics. 43:1982;59-69.
12. Kohonen T. Self-organizing maps. 1995;Springer, Heidelberg.
13. Kostiainen T., Lampinen J. Generative probability density model in the self-organizing map. Seiffert U., Jain L., Self-organizing neural networks: Recent advances and applications. 2002;75-94 Physica Verlag, Heidelberg.
14. Linsker R. How to generate ordered maps by maximizing the mutual information between input and output signals. Neural Computation. 1:1989;402-411.
15. Park J., Sandberg I.W. Approximation and radial-basis function networks. Neural Computation. 5:1993;305-316.
16. Sain S.R., Scott D.W. On locally adaptive density estimation. Journal of the American Statistical Association. 91:1996;1525-1534.
17. Silverman B.W. Density estimation for statistics and data analysis. 1992;Chapman and Hall, London.
18. Sum J., Leung C.-S., Chan L.-W., Xu L. Yet another algorithm which can generate topography map. IEEE Transactions on Neural Networks. 8:(5):1997;1204-1207.
19. Utsugi A. Hyperparameter selection for self-organizing maps. Neural Computation. 9:1997;623-635.
20. Van Hulle M.M. Kernel-based equiprobabilistic topographic map formation. Neural Computation. 10:(7):1998;1847-1871.
21. Van Hulle M.M. Faithful representations and topographic maps: From distortion-to information-based self-organization. 2000;Wiley, New York.
22. Van Hulle M.M. Kernel-based topographic map formation by local density modeling. Neural Computation. 14:(8):2002;. in press.
23. Vapnik V.N. The nature of statistical learning theory. 1995;Springer, New York.
24. Weisstein E.W. CRC concise encyclopedia of mathematics. 1999;Chapman and Hall, London.
25. Yin H., Allinson N.M. Self-organizing mixture networks for probability density estimation. IEEE Transactions on Neural Networks. 12:2001;405-411.