Ensembles of RBFs Trained by Gradient Descent

  • Carlos Hernández-Espinosa
  • Mercedes Fernández-Redondo
  • Joaquín Torres-Sospedra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3173)


Building an ensemble of classifiers is an useful way to improve the performance. In the case of neural networks the bibliography has centered on the use of Multilayer Feedforward (MF). However, there are other interesting networks like Radial Basis Functions (RBF) that can be used as elements of the ensemble. Furthermore, as pointed out recently the network RBF can also be trained by gradient descent, so all the methods of constructing the ensemble designed for MF are also applicable to RBF. In this paper we present the results of using eleven methods to construct a ensemble of RBF networks. The results show that the best method is in general the Simple Ensemble.


Radial Basis Function Gradient Descent Radial Basis Function Neural Network Ensemble Method Error Reduction 
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.


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  1. 1.
    Tumer, K., Ghosh, J.: Error Correlation and Error Reduction in Ensemble Classifiers. Connection Science 8(3 & 4), 385–404 (1996)CrossRefGoogle Scholar
  2. 2.
    Raviv, Y., Intrator, N.: Bootstrapping with Noise: An Effective Regularization Technique. Connection Science 8(3 & 4), 355–372 (1996)CrossRefGoogle Scholar
  3. 3.
    Karayiannis, N.B., Randolph-Gips, M.M.: On the Construction and Training of Reformulated Radial Basis Function Neural Networks. IEEE Trans. On Neural Networks. 14(4), 835–846 (2003)CrossRefGoogle Scholar
  4. 4.
    Drucker, H., Cortes, C., Jackel, D., et al.: Boosting and Other Ensemble Methods. Neural Computation 6, 1289–1301 (1994)zbMATHCrossRefGoogle Scholar
  5. 5.
    Freund, Y., Schapire, R.: Experiments with a New Boosting Algorithm. In: Proceedings of the Thirteenth International Conference on Machine Learning, pp. 148–156 (1996)Google Scholar
  6. 6.
    Rosen, B.: Ensemble Learning Using Decorrelated Neural Networks. Connection Science 8(3 & 4), 373–383 (1996)CrossRefGoogle Scholar
  7. 7.
    Auda, G., Kamel, M.: EVOL: Ensembles Voting On-Line. In: Proc. of the World Congress on Computational Intelligence, pp. 1356–1360 (1998)Google Scholar
  8. 8.
    Liu, Y., Yao, X.: A Cooperative Ensemble Learning System. In: Proc. of the World Congress on Computational Intelligence, pp. 2202–2207 (1998)Google Scholar
  9. 9.
    Jang, M., Cho, S.: Ensemble Learning Using Observational Learning Theory. In: Proceedings of the International Joint Conference on Neural Networks, vol. 2, pp. 1281–1286 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Carlos Hernández-Espinosa
    • 1
  • Mercedes Fernández-Redondo
    • 1
  • Joaquín Torres-Sospedra
    • 1
  1. 1.Dept. de Ingeniería y Ciencia de los ComputadoresUniversidad Jaume ICastellonSpain

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