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Statistical analysis of the main parameters in the definition of Radial Basis Function networks

  • I. Rojas
  • O. Valenzuela
  • A. Prieto
Methodology for Data Analysis, Task Selection and Nets Design
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1240)

Abstract

As there are many possibilities to select the set of basic functions, parameters and operators used in the design of a Radial Basis Function network (RBF) and in general in Artificial Neural Networks, the search for operators and parameters that are most suitable for the design of an RBF, its characterization and evaluation, is an important topic in the field of Neural Network design. A better insight into the performance of the alternative parameters in the design of an RBF (the distance used, the number of neurons and their nonlinear function in the hidden layer, the number of bits used for weight storage, etc) would make it easier to develop a practical application that uses this type of neural network. In the present contribution, the relevance and relative importance of the parameters involved in the design of an RBF are investigated by using a statistical tool, the ANalysis Of the VAriance (ANOVA)[9]. In order to analyzed the behaviour of the RBF, three different examples were used: the recognition of 26 different letters represented as a 5 by 7 grid of integer values, chaos time-series prediction using the Mackey-Glass differential equation and finally function estimation from samples. This methodology can also be applied to others Neural Networks. The results obtained show that the type of function in the hidden layer and the distance used are the most relevant factors in the behaviour of an RBF. Moreover, this statistical analysis is able to establish a classification of latter factors according to their intrinsic characteristics.

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References

  1. [1]
    M.Bianchini, P.Frasconi, M.Gori, “Learning without Local Minima in Radial Basis Function Networks”, IEEE Transaction on Neural Networks, vol.6,no.3, pp.749–756, May 1995.Google Scholar
  2. [2]
    A.G.Bors, I.Pitas, “Median Radial Basis Function Neural Network”, IEEE Transaction on Neural Networks, vol.7,no.6, pp.1351–1364, November 1996.Google Scholar
  3. [3]
    R.L.Hardy, “Multiquadratic equations of topography and other irregular surfaces”, J.Geophys. Res., vol.76, pp.1905–1915, 1971.Google Scholar
  4. [4]
    M.Brown, C.Harris, “Neurofuzzy Adaptive Modelling and Control”, Englewood Cliffs, NJ: Prentice-Hall, 1994.Google Scholar
  5. [5]
    G.Casella, R.L.Berger, “Statistical Inference”, Duxbury Press, 1990Google Scholar
  6. [6]
    V.Cherkassky, D.Gehring, F.Mulier, “Comparison of Adaptive Methods for Function Estimation from Samples”, IEEE Tran. on Neural Networks, vol.7,no.4, pp.969–984, 1996.Google Scholar
  7. [7]
    R.Dogaru, A.T.Murgan, S.Ortmann, M.Glesner, “A Modified RBF Neural Network for efficient current-mode VLSI implementation”, Proceedings of MicroNeuro'96, pp.265–270, 1996.Google Scholar
  8. [8]
    S.Elanayar, Y.C.Shin, “Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems”, IEEE Tran. on Neural Networks, Vol.5, No.4, pp.594–603, 1994.Google Scholar
  9. [9]
    D.C.Montgomery, “Design and Analysis of Experiments”. New York: Wiley, 1984.Google Scholar
  10. [10]
    J.Moody, C.Darken, “Fast learning in networks of locally-tuned processing units”, Neural Computa., vol.1, no.2, pp.281–294, 1989.Google Scholar
  11. [11]
    J.Park, I.W.Sandberg, “Universal Approximation Using Radial Basis Function Networks”, Neural Computation, Vol.3, pp.246–247, 1991.Google Scholar
  12. [12]
    B.A.Whitehead, Tinothy.D.Choate, “Cooperative-Competitive Genetic Evolution of Radial Basis Function Centers and Widths for Time Series Prediction”, IEEE Transaction on Neural Networks, vol.7,no.4, pp.869–880, July, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • I. Rojas
    • 1
  • O. Valenzuela
    • 2
  • A. Prieto
    • 1
  1. 1.Departamento de Electrónica y Tecnología de ComputadoresUniversidad de GranadaGranadaSpain
  2. 2.Departamento de Estadística e Investigatión OperativaUniversidad de GranadaGranadaSpain

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