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Self-organising Artifical Neural Networks

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 930))

Abstract

Self-organisation is displayed during the unsupervised learning of the Kohonen Neural Network (KNN) algorithm. Classical Markov techniques, the ordinary differential equation (ODE) method being included among these, have so far not yielded a complete general analysis of self-organisation in the KNN. In order to obtain a more general understanding of self-organising behaviour which could then be applied to the analysis of self-organisation in the KNN two simpler self-organising algorithms are described. The first algorithm is based on a simple intuitive understanding of self-organisation. The second is based on a simplification of the KNN algorithm. Using the ODE method general results on the self-organising abilities of the two algorithms are given.

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References

  1. G. Nicolis and I. Prigogine. Exploring Complexity. W. H. Freeman, New York. 1989.

    Google Scholar 

  2. E. Jantsch. The Self-Organising Universe. Pergamon Press, Oxford, New York, 1980.

    Google Scholar 

  3. T. Kohonen. Speech Recognition based on topology preserving neural maps. Kogan Page, London. 1989.

    Google Scholar 

  4. F. Blayo and P. Desmartines. Kohonen algorithms: Application to the analysis of economic data. Bulletin des Schweizerischen Eletrotechnischen Vereins und des Verbandes Schweizerischer Elektrizitatswerke, 85(5):23–26, 1992. (in French).

    Google Scholar 

  5. E. Parzen. Stochastic Processes. Holden-Day, Inc., San Francisco, London, Amsterdam, 1962.

    Google Scholar 

  6. M. Cottrell and J.C. Fort. Étude d'un processus d'auto-organisation. Ann. Inst. Henri Poincaré, 23(1):1–20, Jan. 1987.

    Google Scholar 

  7. C. Bouton and G. Pagès. Self-organisation of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli. Stochastic Processes and their Applications, 47:249–274, 1993.

    Google Scholar 

  8. E. Erwin, K. Obermayer, and K. Schulten. Self-organising maps: Ordering, convergence properties and energy functions. Biol. Cybern., 67:47–55, 1992.

    PubMed  Google Scholar 

  9. P. Thiran and M. Hasler. Self-organisation of a one dimensional Kohonen network with quantized weights and inputs. To appear in Neural Networks.

    Google Scholar 

  10. M. Cottrell, J.C. Fort, and G. Pagès. Two or three things we know about the Kohonen algorithm. In Proceedings of ESANN, 1994.

    Google Scholar 

  11. John A. Flanagan. Self-organising neural networks, 1994. Thèse no 1306 (1994) Electricity Department, EPFL, Lausanne, Switzerland.

    Google Scholar 

  12. L. Ljung. Analysis of recursive stochastic algorithms. IEEE Trans. on Automatic Control, AC-22(4):551–575, Aug. 1977.

    Google Scholar 

  13. H. J. Kushner and D. S. Clark. Stochastic Approximation Methods for Constrained and Unconstrained Systems, volume 26 of Applied Mathematical Sciences. Springer-Verlag, New York, Heidelberg, Berlin, 1978.

    Google Scholar 

  14. C. Bouton and G. Pagès. Convergence in distribution of the one-dimensional Kohonen algorithm when the stimuli are not uniform. Advances in Applied Probability, 26(1), March 1994.

    Google Scholar 

  15. M. Cottrell and J.C. Fort. A stochastic model of retinotopy: A self organising process. Biol. Cybern., 53:405–411, 1986.

    PubMed  Google Scholar 

  16. W. Kaplan. Advanced Mathematics for Engineers. Addison-Wesley, New York, 1981.

    Google Scholar 

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José Mira Francisco Sandoval

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© 1995 Springer-Verlag Berlin Heidelberg

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Flanagan, J.A., Hasler, M. (1995). Self-organising Artifical Neural Networks. In: Mira, J., Sandoval, F. (eds) From Natural to Artificial Neural Computation. IWANN 1995. Lecture Notes in Computer Science, vol 930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59497-3_192

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  • DOI: https://doi.org/10.1007/3-540-59497-3_192

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59497-0

  • Online ISBN: 978-3-540-49288-7

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