Sequential learning algorithm for PG-RBF network using regression weights for time series prediction

  • I. Rojas
  • H. Pomares
  • Juris L. Bernier
  • Juris Ortega
  • E. Ros
  • A. Prieto
Plasticity Phenomena (Maturing, Learning & Memory)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1606)


We propose a modified radial basis function network (RBF) in which the main characteristics are that: a) the gaussian function is modified using pseudo-gaussian (PG) in which two scaling parameters σ are introduced; b) the activation of the hidden neurons is normalized c) instead of using a single parameter for the output weights, these are functions of the input variables; d) a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. It is shown that the modified PG-RBF can reduce the number of didden units significantly compared with the classical RBF network. The feasibility of the resulting algorithm for the neural network to evolve and learn is demonstrated by predicting time series.


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  1. [1]
    N. B. Karayiannis, G. Weiqun Mi, “Growing Radial Basis Neural Networks: Merging Supervised and Unsupervised Learning with Network Growth Techniques”, IEEE Transaction on Neural Networks, vol.8, no. 6, pp. 1492–1506, November 1997.CrossRefGoogle Scholar
  2. [2]
    J. E. Moody, C. J. Darke, “Fast learning in networks of locally-tuned processing units”, Neural Computa., vol. 1, pp. 281–294, 1989.CrossRefGoogle Scholar
  3. [3]
    J. Platt, “A resource allocating network for function interpolation”, Neural Computa., vol. 3, pp. 213–225, 1991.MathSciNetCrossRefGoogle Scholar
  4. [4]
    L. Yingwei, N. Sundarajan, P. Saratchandran, “Performance Evaluation of a Sequential Minimal Radial Basis Function (RBF) Neural Network Learning Algorithm”, IEEE Transactions on Neural Networks, vol. 9, no. 2, pp. 308–318, March 1998.CrossRefGoogle Scholar
  5. [5]
    S. Chen, C. F. N. Cowan, P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks”, IEEE Trans. Neural Networks 2 (2), pp. 302–309, 1991.CrossRefGoogle Scholar
  6. [6]
    S. Haykin, Neural Networks-A Comprehensive Foundation, IEEE Press, New York, 1994.MATHGoogle Scholar
  7. [7]
    H. Surmann, A. Kanstein, K. Goser “Self-organizing and genetic algorithms for an automatic design of fuzzy control and decision systems”, Proc. of EUFIT 93.Google Scholar
  8. [8]
    T. Kohonen, Self-Organization and Associative Memory, Springer, New York, 1988.CrossRefMATHGoogle Scholar
  9. [9]
    A. Sherstinsky, R. W. Picard, “On the efficiency of the orthogonal least squares training method for radial basis function networks”, IEEE Trans. Neural Networks vol. 7, no. 1, pp. 195–200, 1996.CrossRefGoogle Scholar
  10. [10]
    D. S. Broomhead, D. Lowe, “Multivariable functional interpolation and adaptive networks”, Complex Syst., vol. 2, pp. 321–355, 1988.MathSciNetMATHGoogle Scholar
  11. [11]
    I. Rojas, M. Anguita, E. Ros, H. Pomares, O. Valenzuela, A. Prieto,: “What are the main factors involved in the design of a Radial Basis Function Network?”, 6th European Symposium on Artificial Neural Network, ESANN’98, pp. 1–6, April 22–24, 1998.Google Scholar
  12. [12]
    F. Anouar, F. Badran, S. Thiria, “Probabilistic self-organizing maps and radial basis function networks”, Neurocomputing, vol. 20, pp. 83–96, 1998.CrossRefMATHGoogle Scholar
  13. [13]
    M. Benaim, “On functional approximation with normalized Gaussian units”, Neural Comput. Vol. 6, 1994Google Scholar
  14. [14]
    S. Nowlan, “Maximum likelihood competitive learning”, Proc. Neural Inform. Process. Systems, pp. 574–582, 1990.Google Scholar
  15. [15]
    J. S. R. Jang, C. T. Sun, E. Mizutani, “Neuro-Fuzzy and soft computing”, Prentice Hall, ISBN 0-13-261066-3, 1997.Google Scholar
  16. [16]
    G. Bugmann, “Normalized Gaussian Radial Basis Function Networks”, Neurocomputing, vol. 20, pp. 97–110, 1998.CrossRefGoogle Scholar
  17. [17]
    I. Rojas, O. Valenzuela, A. Prieto, “Statistical analysis of the main parameters in the definition of Radial Basis Function Networks”, Lecture Notes in Computer Science, Vol. 1240, pp. 882–891, Springer-Verlag, June 1997.CrossRefGoogle Scholar
  18. [18]
    S. Lee, R. M. Kil, “A Gaussian potential function network with hierarchically self-organizing learning”, Neural Network, vol. 2, pp. 207–224, 1991.CrossRefGoogle Scholar
  19. [19]
    M. T. Musavi, W. Ahmed, K. H. Chan, K. B. Faris, D. M. Hummels, “On the training of radial basis function classifier”, Neural Networks, vol. 5, pp. 595–603, 1992.CrossRefGoogle Scholar
  20. [20]
    V. Kadirkamanathan, M. Niranjan, “A function estimation approach to sequential learning with neural networks”, Neural Computa., vol. 5, pp. 954–975, 1993.CrossRefGoogle Scholar
  21. [21]
    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.CrossRefGoogle Scholar
  22. [22]
    S.-H. Lee, I. Kim, “Time series analysis using fuzzy learning”, in Proc. Int. Conf. Neural Inform. Processing, Seoul, Korea., pp. 1577–1582, vol. 6, Oct. 1994.Google Scholar
  23. [23]
    C. J. Lin, C. T. Lin, “An ART-Based fuzzy adaptive learning control network”, IEEE Transactions on Fuzzy Systems vol. 5, no. 4, pp. 477–496, November 1997.CrossRefGoogle Scholar
  24. [24]
    D. Kim, C. Kim, “Forecasting time series with genetic fuzzy predictor ensemble”, IEEE Transactions on Fuzzy Systems vol. 5, no. 4, pp. 523–535, November 1997.CrossRefGoogle Scholar
  25. [25]
    R. S. Crowder III, “Predicting the Mackey-Glass time series with cascadecorrelation learning”, In D. Touretzky, G. Hinton and T. Sejnowski, editors, Proceedings of the 1990 Connectionist Model Summer School, pages 117–123, Carnegic Mellon University, 1990.Google Scholar
  26. [26]
    K. B. Cho, B. H. Wang, “Radial basis function based adaptive fuzzy systems and their applications to system identification and prediction”, Fuzzy Sets and Systems, vol. 83, pp. 325–339, 1995.MathSciNetCrossRefGoogle Scholar
  27. [27]
    L. X. Wang, J. M. Mendel, “Generating fuzzy rules by learning from examples”, IEEE Trans. On Syst. Man and Cyber vol. 22, no. 6, November/December, pp. 1414–1427, 1992.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • I. Rojas
    • 1
  • H. Pomares
    • 1
  • Juris L. Bernier
    • 1
  • Juris Ortega
    • 1
  • E. Ros
    • 1
  • A. Prieto
    • 1
  1. 1.Department of Architecture and Computer TechnologyUniversity of GranadaSpain

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