Abstract
We propose a two-staged fuzzy clustering algorithm to train radial basis function neural networks. The novelty of the contribution lies in the way we handle the input training data information between the two stages of the algorithm. The back-propagation method is employed to optimize the network parameters. The number of hidden nodes is determined by the iterative implementation of the fuzzy clustering and the back-propagation. Simulation results show that the methodology produces accurate models compared to the standard and more sophisticated techniques reported in the literature.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Luo, W., Karim, M.N., Morris, A., Martin, E.B.: Control Relevant Identification of a pH Wastewater Neutralisation Process using Adaptive Radial Basis Function Networks. Computers and Chemical Engineering, S1017 (1996)
Narendra, K.S., Parthasarathy, K.: Identification and Control of Dynamical Systems Using Neural Networks. IEEE Trans. Neural Networks 1, 4 (1990)
Leonard, J.A., Kramer, M.A.: Radial Basis Function Networks for Classifying Process Faults. IEEE Control Systems 31 (1991)
Lazaro, M., Santamaria, I., Pantaleon, C.: A new EM-based training algorithm for RBF networks. Neural Networks 16(1), 69–77 (2003)
Sarimveis, H., Alexandridis, A., Tsekouaras, G., Bafas, G.: A Fast and Efficient Algorithm for Training Radial Basis Function Neural Networks Based on a Fuzzy Partition of the Input Space, Ind. Eng. Chem. Research 41, 751–759 (2002)
Lucks, M.B., Oki, N.: A Radial Basis Network for Function Approximation. In: The Proceedings of the 42nd Midwest Symposium on Circuits and Systems, pp. 1099–1101 (1999)
Figueiredo, M.A.: On Gaussian Radial Basis Function Approximations: Interpretation, Extensions and Learning Strategies, pp. 618–621 (2000)
Karayiannis, N.B.: Reformulated radial basis neural networks trained by gradient descent. IEEE Transactions on Neural Networks 10(3), 657–671 (1999)
Gonzalez, J., Rojas, I., Ortega, J., Pomares, H., Fernandez, J., Diaz, A.F.: 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)
Babuska, R., Verbruggen, H.: Neuro-fuzzy methods for nonlinear system identification. Annual Reviews in Control 27, 73–85 (2004)
Pedrycz, W.: Conditional Fuzzy Clustering in the Design of Radial Basis Function Neural Networks. IEEE Trans. Neural Networks 9(4), 601–612 (1998)
Staiano, A., Tagliaferri, R., Pedrycz, W.: Improving RBF Networks Performance in Regression Tasks by Means of a Supervised Fuzzy Clustering. Neurocomputing 69, 1570–1581 (2006)
Tsekouras, G.: On the use of the weighted fuzzy c-means in fuzzy modeling. Adv. Eng. Softw. 36, 287–300 (2005)
Linkens, D.A., Chen, M.: Input selection and partition validation for fuzzy modelling using neural network. Fuzzy Sets Syst. 107, 299–308 (1999)
Cho, K.B., Wang, B.H.: Radial basis function based adaptive fuzzy systems their application to system identification and prediction. Fuzzy Sets and Systems 83, 325–339 (1995)
Kim, D., Kim, C.: Forecasting time series with genetic fuzzy predictor ensembles. IEEE Trans. Fuzzy Systems 5, 523–535 (1997)
Chen, Y., Yang, B., Dong, J., Abraham, A.: Time-series Forecasting using Flexible Neural Tree Model. Information Science 174, 219–235 (2005)
Chen, Y., Yang, B., Zhou, J.: Automatic Design of Hierarchical RBF Networks for System Identification, pp. 1191–1199 (2006)
Jang, J.-S.R., Sun, C.-T., Mizutani, E.: Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence. Prentice-Hall, Upper Saddle River (1997)
Chen, S., Cowan, C.F.N., Grant, P.M.: Orthogonal least squares learning algorithm for radial basic function network. IEEE Trans. Neural Networks 2, 302–309 (1991)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Niros, A.D., Tsekouras, G.E. (2008). A Fuzzy Clustering Algorithm to Estimate the Parameters of Radial Basis Functions Neural Networks and Its Application to System Modeling. In: Darzentas, J., Vouros, G.A., Vosinakis, S., Arnellos, A. (eds) Artificial Intelligence: Theories, Models and Applications. SETN 2008. Lecture Notes in Computer Science(), vol 5138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87881-0_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-87881-0_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87880-3
Online ISBN: 978-3-540-87881-0
eBook Packages: Computer ScienceComputer Science (R0)