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Towards an information-theoretic approach to kernel-based topographic map formation

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Abstract

A new information-theoretic learning scheme is introduced for kernel-based topographic map formation. The kernel parameters are adjusted so as to maximize the differential entropies of the kernel outputs and, at the same time, to minimize the mutual information between these outputs. The learning scheme is based on infomax learning supplemented with a cooperative/competitive stage to achieve topographically-organized maps. As a potential application, we consider density estimation.

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References

  1. Kohonen, T. (1982) Self-organized formation of topologically correct feature maps. Biol. Cybern., 43, 59–69

    Article  MathSciNet  MATH  Google Scholar 

  2. Kohonen, T. (1995) Self-organizing maps. Springer, Berlin Heidelberg

    Google Scholar 

  3. Durbin, R., Willshaw, D. (1987) An analogue approach to the travelling salesman problem using an elastic net method. Nature, 326, 689–691

    Article  Google Scholar 

  4. Graepel, T., Burger, M., Obermayer, K. (1997) Phase transitions in stochastic self-organizing maps. Physical Rev. E, 56(4), 3876–3890

    Article  Google Scholar 

  5. Sum, J., Leung, C.-S., Chan, L.-W., Xu, L. (1997) Yet another algorithm which can generate topography map. IEEE TNNS, 8(5), 1204–1207

    Google Scholar 

  6. Bishop, C.M., Svensæn, M., Williams, C.K.I. (1998) GTM: The generative topographic mapping. Neural Computat., 10, 215–234

    Article  Google Scholar 

  7. Van Hulle, M.M. (1998) Kernel-based equiprobabilistic topographic map formation. Neural Computat., 10(7), 1847–1871

    Article  Google Scholar 

  8. Van Hulle, M.M. (2000) Faithful representations and topographic maps: From distortion- to information-based self-organization, Wiley, New York

    Google Scholar 

  9. András, P. (2001) Kernel-Kohonen networks. Int. J. Neural Systems, submitted

    Google Scholar 

  10. Linsker, R. (1989) How to generate ordered maps by maximizing the mutual information between input and Output signals. Neural Computat., 1, 402–411

    Article  Google Scholar 

  11. Bell A.J., Sejnowski, T.J. (1995) An information-maximization approach to blind Separation and blind deconvolution. Neural Computat., 7, 1129–1159

    Article  Google Scholar 

  12. Weisstein, E.W. (1999) CRC Concise Encyclopedia of Mathematics. Chapman and Hall, London

    Google Scholar 

  13. Silverman, B.W. (1992) Density estimation for statistics and data analysis. Chapman and Hall, London

    Google Scholar 

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© 2001 Springer-Verlag London Limited

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Van Hulle, M.M. (2001). Towards an information-theoretic approach to kernel-based topographic map formation. In: Advances in Self-Organising Maps. Springer, London. https://doi.org/10.1007/978-1-4471-0715-6_1

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  • DOI: https://doi.org/10.1007/978-1-4471-0715-6_1

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-511-3

  • Online ISBN: 978-1-4471-0715-6

  • eBook Packages: Springer Book Archive

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