Abstract
In this paper, we propose a differential evolution algorithm based design for the beta basis function neural network. The differential Evolution algorithm has been used in many practical cases and has demonstrated good convergences properties. The differential evolution is used to evolve the beta basis function neural networks topology. Compared with the traditional genetic algorithm, the combined approach proves goodly the difference, including the feasibility and the simplicity of implementation. In the prediction of Mackey-Glass chaotic time series, the networks designed by the proposed approach prove to be competitive, or even superior, to the traditional learning algorithm for a multi-layer Perceptron network and radialbasis function network. Therefore, designing a set of BBFNN can be considered as solution of a two-optimisation problem.
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References
M.A. Alimi : The Beta System: Toward a Change in Our Use of Neuro-Fuzzy Systems, International Journal of Management, Invited Paper, June 2000, 15–19.
M.A. Alimi : On-Line Analysis of Handwritten Arabic. A New Approach to Recognize Segmented Characters From Cursive Script, Les Annales Maghrbines de l’Ingnieur, vol. 14, no.1 (2000), 7–27.
M.A. Alimi, R. Hassine and M. Selmi : Beta Fuzzy Logic Systems: Approximation Properties in the SISO Case, International Journal of Applied Mathematics & Computer Science, Special Issue on “Neuro-Fuzzy and Soft Computing” edited by D. Rutkowska and L.A. Zadeh, vol. 10, no. 4 (2000), 857–875.
M.A. Alimi and M. Ben Jemaa, Beta Fuzzy Neural Network Application in Recognition of Spoken Isolated Arabic Words, Journal of Control and Intelligent Systems, Special Issue on Non-linear Speech Processing Techniques and Applications, vol. 30, no. 2, (2002), 47–51.
M.A. Alimi, R. Hassine and M. Selmi, Beta Fuzzy Logic Systems: Approximation Properties in the SISO Case, International Journal of Applied Mathematics and Computer Science, Special Issue on Neuro-Fuzzy and Soft Computing edited by D. Rutkowska and L.A. Zadeh, vol. 10, no. 4 (2000), 857–875.
C. Aouiti, M.A. Alimi and A. Maalej, A Genetic Designed Beta Basis Function Neural Network for Approximating Multi-Variables Functions, in V. Kurkova et al. (eds.) Artificial Neural Nets and Genetic Algorithms, Springer-Verlag, Wien, (2001), 383–386.
C. Aouiti, M.A. Alimi, F. Karray and A. Maalej, A Hierarchical Genetic Algorithm For The Design Of Beta Basis Function Neural Network, Proc. International Joint Conference on Neural Networks: IJCNN02, Honolulu, Hawaii, May 2002.
C. Aouiti, A.M. Alimi and A. Maalej, A Genetic Designed Beta Basis Function Neural Networks for Multivariable Functions Approximation, Systems Analysis, Modeling, and Simulation, Special Issue on Advances in Control and Computer Engineering, vol. 42, no. 7 (2002), 975–1005.
H. Bezine, M.A. Alimi and N. Derbel, Handwriting Trajectory Movements Controlled by a Beta-Elliptic Model, Proc. 7th International Conference on Document Analysis and Recognition: ICDAR’2003, Edinburgh, UK, August 2003, 1228–1232.
H. Dhahri, and M.A. Alimi, The Modified Differential Evolution and the RBF (MDE-RBF) Neural Network for Time Series Prediction Proc. International Joint Conference on Neural Networks: IJCNN06, Vancouver, July 2006, 5245–5250.
H. Dhahri and M.A. Alimi, Hierarchical Learning Algorithm for the Beta Basis Function Neural Network, Proc. Third International Conference on Systems, Signals and Devices: SSD05, Sousse, Tunisia, March 2005.
J. Gonzalez, I. Rojas, J. Ortega, H Pomares and et al.,: Multiobjective evolutionary of the size, shape and position parameter of radial basis function neural network for function approximation, IEEE Trans. Neural Netw., vol. 14, no. 6 (2003), 1478–1495.
M.T. Hamdani and M.A. Alimi, Beta-SVM a new Support Vector Machine Kernel, Proc. International Conference on Artificial Neural Networks and Genetic Algorithms: ICANNGA03, Roanne, France, April 2003, 63–68.
T. Hamdani and M.A. Alimi : how SVM a New Support Vector Machine Kernel, in D.W. Pearson, N.C. Steele, and R.F. Albrecht (eds.) Artificial Neural Nets and Genetic Algorithms, Springer-Verlag, Wien, (2003), pp. 63–68.
M.T. Hamdani and M. A. Alimi, How are beta-SVM good kernels, Proc. World Computer Congres: WCC’2004, Toulouse, France, pp. 283–292.
R. Hassine, M.A. Alimi and M. Selmi A Constructive Learning Algorithm for Beta Fuzzy Logic Systems, Proc. Int. Conf. Computational and Artificial Intelligence for Decision, Control and Automation: ACIDCA’00, Monastir, Tunisia, March 2000, 72–75.
R. Hassine, F. Karray, M. A. Alimi and M. Selmi, Approximation Properties of Fuzzy Systems for Smooth Functions and Their First Order Derivative, IEEE Trans. Systems, Man and Cybernetics, Part A, vol. 33, no. 2 (2003), pp. 160–168.
G. Huang, P. Saratchandran and N. Sundararajan, A Generalized Growing and Pruning RBF Neural Network for Function Approximation IEEE Trans. Neural Netw. 16, 1 (2005).
M. Kherallah, M.A. Alimi and N. Derbel, On-Line recognition of handwritten digits by Self organisation maps using elliptical and beta representations, Proc. Premier Congrs International de Signaux, Circuits et Systmes: SCS’04, Monastir, Tunisie, (2004), 503–507.
M. Kherallah, L. Haddad and M.A. Alimi, Towards the design of handwriting recognition system by neuro-fuzzy and beta elliptical approaches, Proc. World Computer Congres: WCC’04, Toulouse, France, (2004),187–196.
M. Kherallah, F. Bouri and M.A. Alimi, Toward an On-Line Handwriting Recognition System Based on Visual Coding and Genetic Algorithm, Proc. International Conference on Artificial Neural Networks and Genetic Algorithms: ICANNGA’2005, Coimbra, Portugal, March, 502–505.
M. Masmoudi, M. Samet and M.A Alimi : A bipolar implementation of the Beta Neuron, International Journal of Electronics, vol. 87, no. 6 (2000), 675–682.
M. Njah, M.A. Alimi, M. Chtourou and R. Tourki, Algoritm of Maximal Descent AMD for training Radial Basis Function Neural Networks, Proc. IEEE International Conference on Systems, Man and Cybernetics: SMC’02, Hammamet, Tunisia, October 2002.
R. Storn and K. Price : Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR-95-012, ICSI, (1999).
R. Storn and K. Price, Differential evolution - A simple and efficient heuristic for global over continuous spaces, J. Global Optimiz., vol 11 (1997), 341–359.
J. Sun, Q. Zhang and E.Tsang DE/EDAA new evolutionary algorithm for global optimisation, Info. Sci., vol.169, (2004), 249–269.
G. Yen and H. Lu, Hierarchical Genetic Algorithm for near optimal Feedforward Neural Network Design, IntJour of Neu. Syst, Vol. 12 (2002), 31–43.
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Dhahri, H., Alimi, A. (2008). Automatic Selection for the Beta Basis Function Neural Networks. In: Krasnogor, N., Nicosia, G., Pavone, M., Pelta, D. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2007). Studies in Computational Intelligence, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78987-1_42
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DOI: https://doi.org/10.1007/978-3-540-78987-1_42
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