Centre and Variance Selection for Gaussian Radial Basis Function Artificial Neural Networks

  • F. Scheibel
  • N. C. Steele
  • R. Low
Conference paper


The quality of the response of a RBF neural network depends strongly on the calculation method of the centres and the variance matrices. This paper describes an algorithm which combines the calculation of the centres and variances of the Gaussian nodes to improve the response of a RBF neural network. The selection of the centres is made using a modified version of the K-means algorithm and the variances are based on the sample variance-covariance matrices of the input values associated with the centres. Applications to classification and function approximation problems are considered.


Hide Layer Fuzzy Controller Output Node Fuzzy Cluster Centre Vector 
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  1. [1]
    Dempster A P., Laird N M and Rubin D B: Maximum Liklehood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society B 39, 1 pp 1–38, 1977.MathSciNetGoogle Scholar
  2. [2]
    Bishop C M: Neural Networks for Pattern Recognition. Oxford University Press, Oxford, 1995.Google Scholar
  3. [3]
    Godjevac J: Neuro-Fuzzy Controllers, Design and Application, Presses Polytechniques et Universitaires Romandes, Lausanne, 1997Google Scholar
  4. [4]
    Moody J and Darken C J: Fast Learning in Networks of Locally-tuned Processing Units. Neural Computation 1, 2, pp 281–294, 1989.CrossRefGoogle Scholar
  5. [5]
    Steele N., Godjevac J: Adaptive Radial Basis Fumction Neural Networks and Fuzzy Systems. Proc CES A′96 Symposium on Discrete Events and Manufacturing Systems, Lille, France, pp 143–148, 1996.Google Scholar
  6. [6]
    Babuska R: Fuzzy Modeling for Control, Kluwer Academic Publishers, Boston, 1998.CrossRefGoogle Scholar
  7. [7]
    Albrecht R., Werner W: Ein Verfahren zur Identifizierung von Zeichen, deren Wiedergabe sta-tionaeren statistischen Stoerungen unterworfen ist. Computing, 1, 1, pp 1–7, 1966.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Gustafson D., Kessel W: Fuzzy Clustering with a Fuzzy Covariance Matrix. Proc IEEE CDC, San Diego, CA, USA, pp 761–766, 1979.Google Scholar

Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • F. Scheibel
    • 1
  • N. C. Steele
    • 2
  • R. Low
    • 2
  1. 1.Fachhochschule DarmstadtDarmstadtGermany
  2. 2.Coventry UniversityCoventryUK

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