Advertisement

Improving Clustering Technique for Functional Approximation Problem Using Fuzzy Logic: ICFA Algorithm

  • A. Guillén
  • I. Rojas
  • J. González
  • H. Pomares
  • L. J. Herrera
  • O. Valenzuela
  • A. Prieto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3512)

Abstract

Clustering algorithms have been applied in several disciplines successfully. One of those applications is the initialization of Radial Basis Functions (RBF) centers composing a Neural Network, designed to solve functional approximation problems. The Clustering for Function Approximation (CFA) algorithm was presented as a new clustering technique that provides better results than other clustering algorithms that were traditionally used to initialize RBF centers. Even though CFA improves performance against other clustering algorithms, it has some flaws that can be improved. Within those flaws, it can be mentioned the way the partition of the input data is done, the complex migration process, the algorithm’s speed, the existence of some parameters that have to be set in order to obtain good solutions, and the convergence is not guaranteed. In this paper, it is proposed an improved version of this algorithm that solves the problems that its predecessor has using fuzzy logic successfully. In the experiments section, it will be shown how the new algorithm performs better than its predecessor and how important is to make a correct initialization of the RBF centers to obtain small approximation errors.

Keywords

Cluster Algorithm Fuzzy Logic Radial Basis Function Input Vector Normalize Root Mean Square Error 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, Nueva York (1981)zbMATHGoogle Scholar
  2. 2.
    Bors., A.G.: Introduction of the Radial Basis Function (RBF) networks. OnLine Symposium for Electronics EngineersGoogle Scholar
  3. 3.
    Duda, R.O., Hart, P.E.: Pattern classification and scene analysis. Wiley, New York (1973)zbMATHGoogle Scholar
  4. 4.
    Gersho, A.: Asymptotically Optimal Block Quantization. IEEE Transanctions on Information Theory 25(4), 373–380 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    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
  6. 6.
    Hartigan, J.A.: Clustering Algorithms. Wiley, New York (1975)zbMATHGoogle Scholar
  7. 7.
    Prieto, A., Rojas, I., Anguita, M., Valenzuela, O.: Analysis of the operators involved in the definition of the implication functions and in the fuzzy inference proccess. Int. J. Approximate Reasoning 19, 367–389 (1998)Google Scholar
  8. 8.
    Karayannis, N.B., Mi, G.W.: Growing radial basis neural networks: Merging supervised and unsupervised learning with network growth techniquesGoogle Scholar
  9. 9.
    Park, J., Sandberg, J.W.: Universal approximation using radial basis functions network. Neural Computation 3, 246–257 (1991)CrossRefGoogle Scholar
  10. 10.
    Cai, Y., Zhu, Q., Liu, L.: A global learning algorithm for a RBF networkGoogle Scholar
  11. 11.
    Russo, M., Patané, G.: Improving the LBG Algorithm. In: Mira, J. (ed.) IWANN 1999. LNCS, vol. 1606, pp. 621–630. Springer, Heidelberg (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

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

Personalised recommendations