Skip to main content
SpringerLink
Log in

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

  • Plasticity Phenomena (Maturing, Learning & Memory)
  • Conference paper
  • First Online:
Foundations and Tools for Neural Modeling (IWANN 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1606))

Included in the following conference series:

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.

    Article  Google Scholar 

  2. J. E. Moody, C. J. Darke, “Fast learning in networks of locally-tuned processing units”, Neural Computa., vol. 1, pp. 281–294, 1989.

    Article  Google Scholar 

  3. J. Platt, “A resource allocating network for function interpolation”, Neural Computa., vol. 3, pp. 213–225, 1991.

    Article  MathSciNet  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  6. S. Haykin, Neural Networks-A Comprehensive Foundation, IEEE Press, New York, 1994.

    MATH  Google Scholar 

  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. T. Kohonen, Self-Organization and Associative Memory, Springer, New York, 1988.

    Book  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  10. D. S. Broomhead, D. Lowe, “Multivariable functional interpolation and adaptive networks”, Complex Syst., vol. 2, pp. 321–355, 1988.

    MathSciNet  MATH  Google Scholar 

  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. F. Anouar, F. Badran, S. Thiria, “Probabilistic self-organizing maps and radial basis function networks”, Neurocomputing, vol. 20, pp. 83–96, 1998.

    Article  MATH  Google Scholar 

  13. M. Benaim, “On functional approximation with normalized Gaussian units”, Neural Comput. Vol. 6, 1994

    Google Scholar 

  14. S. Nowlan, “Maximum likelihood competitive learning”, Proc. Neural Inform. Process. Systems, pp. 574–582, 1990.

    Google Scholar 

  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. G. Bugmann, “Normalized Gaussian Radial Basis Function Networks”, Neurocomputing, vol. 20, pp. 97–110, 1998.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  18. S. Lee, R. M. Kil, “A Gaussian potential function network with hierarchically self-organizing learning”, Neural Network, vol. 2, pp. 207–224, 1991.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  20. V. Kadirkamanathan, M. Niranjan, “A function estimation approach to sequential learning with neural networks”, Neural Computa., vol. 5, pp. 954–975, 1993.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Architecture and Computer Technology, University of Granada, Spain

    I. Rojas, H. Pomares, Juris L. Bernier, Juris Ortega, E. Ros & A. Prieto

Authors
  1. I. Rojas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Pomares
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Juris L. Bernier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Juris Ortega
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. E. Ros
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. Prieto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

José Mira Juan V. Sánchez-Andrés

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rojas, I., Pomares, H., Bernier, J.L., Ortega, J., Ros, E., Prieto, A. (1999). Sequential learning algorithm for PG-RBF network using regression weights for time series prediction. In: Mira, J., Sánchez-Andrés, J.V. (eds) Foundations and Tools for Neural Modeling. IWANN 1999. Lecture Notes in Computer Science, vol 1606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098221

Download citation

  • DOI: https://doi.org/10.1007/BFb0098221

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66069-9

  • Online ISBN: 978-3-540-48771-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation