A Fuzzy-Possibilistic Fuzzy Ruled Clustering Algorithm for RBFNNs Design

  • A. Guillén
  • I. Rojas
  • J. González
  • H. Pomares
  • L. J. Herrera
  • A. Prieto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4259)


This paper presents a new approach to the problem of designing Radial Basis Function Neural Networks (RBFNNs) to approximate a given function. The presented algorithm focuses in the first stage of the design where the centers of the RBFs have to be placed. This task has been commonly solved by applying generic clustering algorithms although in other cases, some specific clustering algorithms were considered. These specific algorithms improved the performance by adding some elements that allow them to use the information provided by the output of the function to be approximated but they did not add problem specific knowledge. The novelty of the new developed algorithm is the combination of a fuzzy-possibilistic approach with a supervising parameter and the addition of a new migration step that, through the generation of RBFNNs, is able to take proper decisions on where to move the centers. The algorithm also introduces a fuzzy logic element by setting a fuzzy rule that determines the input vectors that influence each center position, this fuzzy rule considers the output of the function to be approximated and the fuzzy-possibilistic partition of the data.


Cluster Algorithm Radial Basis Function Input Vector Fuzzy Rule Radial Basis Function Neural Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)MATHGoogle Scholar
  2. 2.
    Bors, A.G.: Introduction of the Radial Basis Function (RBF) networks. In: OnLine Symposium for Electronics Engineers, February 2001, vol. 1, pp. 1–7 (2001)Google Scholar
  3. 3.
    Cherkassky, V., Lari-Najafi, H.: Constrained topological mapping for nonparametric regression analysis. Neural Networks 4(1), 27–40 (1991)CrossRefGoogle Scholar
  4. 4.
    Friedman, J.H.: Multivariate adaptive regression splines (with discussion). Annals of Statistics 19, 1–141 (1991)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Friedman, J.H.: Projection pursuit regression. Journal of the American Statistical Association 76, 817–823 (1981)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Gersho, A.: Asymptotically Optimal Block Quantization. IEEE Transanctions on Information Theory 25(4), 373–380 (1979)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    González, J., Rojas, I., Ortega, J., Pomares, H., Fernández, F.J., Díaz, A.: Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation. IEEE Transactions on Neural Networks 14(6), 1478–1495 (2003)CrossRefGoogle Scholar
  8. 8.
    González, J., Rojas, I., Pomares, H., Ortega, J., Prieto, A.: A new Clustering Technique for Function Aproximation. IEEE Transactions on Neural Networks 13(1), 132–142 (2002)CrossRefGoogle Scholar
  9. 9.
    Guillén, A., Rojas, I., González, J., Pomares, H., Herrera, L.J., Valenzuela, O., Prieto, A.G.: A Possibilistic Approach to RBFN Centers Initialization. In: Ślęzak, D., Yao, J., Peters, J.F., Ziarko, W.P., Hu, X. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3642, pp. 174–183. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Guillén, A., Rojas, I., González, J., Pomares, H., Herrera, L.J., Valenzuela, O., Prieto, A.G.: Improving Clustering Technique for Functional Approximation Problem Using Fuzzy Logic: ICFA Algorithm. In: Cabestany, J., Prieto, A.G., Sandoval, F. (eds.) IWANN 2005. LNCS, vol. 3512, pp. 272–279. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Karayiannis, N.B., Mi, G.W.: Growing radial basis neural networks: Merging supervised and unsupervised learning with network growth techniques. IEEE Transactions on Neural Networks 8, 1492–1506 (1997)CrossRefGoogle Scholar
  12. 12.
    Pal, N.R., Pal, K., Bezdek, J.C.: A Mixed C–Means Clustering Model. In: Proceedings of the 6th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 1997), Barcelona, July 1997, vol. 1, pp. 11–21 (1997)Google Scholar
  13. 13.
    Park, J., Sandberg, J.W.: Universal approximation using radial basis functions network. Neural Computation 3, 246–257 (1991)CrossRefGoogle Scholar
  14. 14.
    Patanè, G., Russo, M.: The Enhanced-LBG algorithm. Neural Networks 14(9), 1219–1237 (2001)CrossRefGoogle Scholar
  15. 15.
    Rojas, I., Anguita, M., Prieto, A., Valenzuela, O.: Analysis of the operators involved in the definition of the implication functions and in the fuzzy inference proccess. International Journal of Approximate Reasoning 19, 367–389 (1998)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Zhang, J., Leung, Y.: Improved possibilistic C–means clustering algorithms. IEEE Transactions on Fuzzy Systems 12, 209–217 (2004)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Zhu, Q., Cai, Y., Liu, L.: A global learning algorithm for a RBF network. Neural Networks 12, 527–540 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • A. Guillén
    • 1
  • I. Rojas
    • 1
  • J. González
    • 1
  • H. Pomares
    • 1
  • L. J. Herrera
    • 1
  • A. Prieto
    • 1
  1. 1.Department of Computer Architecture and TechnologyUniversidad de GranadaSpain

Personalised recommendations