Skip to main content
SpringerLink
Log in

Linguistic Rule Extraction From a Simplified RBF Neural Network

  • Published:
Computational Statistics Aims and scope Submit manuscript

Summary

Representing the concept of numerical data by linguistic rules is often desirable. In this paper, we present a novel rule-extraction algorithm from the radial basis function (RBF) neural network classifier for representing the hidden concept of numerical data. Gaussian function is used as the basis function of the RBF network. When training the RBF neural network, we allow for large overlaps between clusters corresponding to the same class, thereby reducing the number of hidden units while improving classification accuracy. The weights connecting the hidden units with the output units are then simplified. The interval for each input in the condition part of each rule is adjusted in order to obtain high accuracy in the extracted rules. Simulations using some bench-marking data sets demonstrate that our approach leads to more accurate and compact rules compared to other methods for extracting rules from RBF neural networks.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1

Similar content being viewed by others

References

  1. Christopher M. Bishop, Neural network for pattern recognition, Oxford University Press, New York, 1995.

    Google Scholar 

  2. T. Brotherton, G. Chadderdon, and P. Grabill, “Automated rule extraction for engine vibration analysis”, Proc. 1999 IEEE Aerospace Conference, vol. 3, pp. 29–38, 1999.

    Article  Google Scholar 

  3. G. Bologna and C. Pellegrini, “Constraining the MLP power of expression to facilitate symbolic rule extraction”, Proc. IEEE World Congress on Computational Intelligence, vol. 1, pp. 146–151, 1998.

    Google Scholar 

  4. LiMin Fu, “Rule Generation from Neural Networks”, IEEE Transaction on systems, man, and cybernetic, Vol. 24, No. 8, August, 1994.

  5. S. K. Halgamuge, W. Poechmueller, A. Pfeffermann, P. Schweikert, and M. Glesner, “A new method for generating fuzzy classification systems using RBF neurons with extended RCE learning Neural Networks”, Proc. IEEE World Congress on Computational Intelligence, vol. 3, pp. 1589–1594, 1994.

    Google Scholar 

  6. E. R. Hruschka and N. F. F. Ebecken, “Rule extraction from neural networks: modified RX algorithm”, Proc. International Joint Conference on Neural Networks, Vol. 4, pp. 2504–2508, 1999.

    Article  Google Scholar 

  7. K.-P. Huber and M. R. Berthold, “Building precise classifiers with automatic rule extraction”, Proc. IEEE International Conference on Neural Networks, vol. 3, pp. 1263–1268, 1995.

    Article  Google Scholar 

  8. H. Ishibuchi, M. Nii, and T. Murata, “Linguistic rule extraction from neural networks and genetic-algorithm-based rule selection”, Proc. International Conference on Neural Networks, vol. 4, pp. 2390–2395, 1997.

    Article  Google Scholar 

  9. H. Ishibuchi and T. Murata, “Multi-objective genetic local search for minimizing the number of fuzzy rules for pattern classification problems”, Fuzzy Systems Proceedings, 1998. IEEE World Congress on Computational Intelligence, vol. 2, pp. 1100–1105, 1998.

    Article  Google Scholar 

  10. P. Maffezzoni and P. Gubian, “Approximate radial basis function neural networks (RBFNN) to learn smooth relations from noisy data”, Proceedings of the 37th Midwest Symposium on Circuits and Systems, vol. 1, pp. 553–556, 1994.

    Article  Google Scholar 

  11. K. J. McGarry, S. Wermter, and J. MacIntyre, “Knowledge extraction from radial basis function networks and multilayer perceptrons”, Proc. International Joint Conference on Neural Networks, vol. 4, pp. 2494–2497, 1999.

    Article  Google Scholar 

  12. K. J. McGarry, J. Tait, S. Wermter, and J. Maclntyre, “Rule-extraction from radial basis function networks”, Proc. Ninth International Conference on Artificial Neural Networks, vol. 2, pp. 613–618, 1999.

    Article  Google Scholar 

  13. K. J. McGarry and J. Maclntyre, “Knowledge extraction and insertion from radial basis function networks”, IEE Colloquium on Applied Statistical Pattern Recognition (Ref. No. 1999/063), pp. 15/1–15/6, 1999.

  14. A. Roy, S. Govil, and R. Miranda, “An algorithm to generate radial basis function (RBF)-like nets for classification problems”, Neural networks, vol. 8, no. 2, pp. 179–201, 1995.

    Article  Google Scholar 

  15. Asim Roy, Sandeep Govil, and Raymond Miranda, “A neural-network learning theory and a polynomial time RBF algorithm”, IEEE Transactions on neural network, vol. 8, NO. 6, pp. 1301–1313, November 1997.

    Article  Google Scholar 

  16. N. Sundararajan, P. Saratchandran, and Y. W. Lu, Radial basis function neural networks with sequential learning: MRAN and its applications, Singapore, River Edge, N.J.: World Scientific, 1999.

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University, Block S2, Nanyang Avenue, Singapore, 639798, Singapore

    Xiuju Fu Ph.D & Lipo Wang

Authors
  1. Xiuju Fu Ph.D
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lipo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiuju Fu Ph.D.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fu, X., Wang, L. Linguistic Rule Extraction From a Simplified RBF Neural Network. Computational Statistics 16, 361–372 (2001). https://doi.org/10.1007/s001800100072

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s001800100072

Keywords

Search

Navigation