Abstract
This paper presents a new evolutionary method to design optimal networks of Radial Basis Functions (RBFs). The main characteristics of this method lie in the estimation of the fitness of a neurone in the population and in the choice of the operator to apply; for this latter objective, a set of fuzzy rules is used. Thus, the estimation of the fitness considered here, is done by considering three main factors: the weight of the neuron in the RBF Network, the overlapping among neurons, and the distances from neurons to the points where the approximation is worst. These factors allow us to define a fitness function in which concepts such as cooperation, speciation, and niching are taken into account. These three factors are also used as linguistic variables in a fuzzy logic system to choose the operator to apply. The proposed method has been tested with the Mackey-Glass series.
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References
M. C. Mackey and L. Glass, “Oscillation and chaos in physiological control system” Sci vol. 197, pp. 287–289, 1.977.
J. Platt, “A resource-allocating network for function interpolation”, Neural Computation 3, 213–225. 1.991
L. Yingwei, N. Sundararajan, P. Saratchandran, “A sequential learning scheme for function approximation using minimal radial basis function neural networks.” Neural Computation 9, 461–478. 1.997
J. Moody and C. Darken, “Fast learning networks of locally-tuned processing units,” Neural Computation, vol. 3 n. 4 pp.579–588, 1.991
Whitehead, B. A.; Choate, T. D.:“Cooperative-competitive genetic evolution of Radial Basis Function centers and widths for time series prediction”. IEEE Trans. on Neural Networks, Vol. 7, No. 4, pp.869–880. July, 1996.
Angeline, P. J.; Saunders, G. M.; Pollack, J. B.:“An evolutionary algorithm that constructs recurrent neural networks”. IEEE Trans. on Neural Networks, Vol. 5, No. 1, pp.54–65. January, 1994.
Maniezzo, V.:“Genetic evolution of the topology and weight distribution of neural networks”. IEEE Trans. on Neural Networks, Vol. 5, No. 1, pp.39–53. January, 1994.
[8] Fahlman, S. E.; Lebiere, C.:“The cascade-correlation learning architecture”. In Advances in Neural Information Processing Systems, 2, Lippmann, P.; Moody, J. E.; and Touretzky, D. S. (eds.), Morgan Kaufmann, pp.524–532, 1991.
Hwang, J.-N.; Lay, S.-R.; Maechler, M.; Martin, R. D.; Schiemert, J.:“Regression modeling in backpropagation and projection pursuit learning”. IEEE Trans. on Neural Networks, Vol. 5, No. 3, pp.342–353. March, 1994.
Smalz, R.; Conrad, M.:“Combining evolution with credit apportionment: a new learning algorithm for neural nets”. Neural Netwroks, Vol. 7, No. 2, pp.341–351, 1994.
[11] Horn, J.; Goldberg, D. E.; Deb, K.:“Implicit niching in learning classifier system: Nature’s way”. Evolutionary Computation, Vol. 2, No. 1, pp.37–66, 1994.
Coello, C. C.:“An Updated Survey of Evolutionary Multiobjective Optimization Techniques: State of the art and future trends”. Congress on Evolutionary Computation, CEC’99, pp.3–13, 1999.
Whitehead, B. A.; Choate, T. D.:“Evolving space-filling curves to distribute radial basis functions over an input space”. IEEE Trans. on Neural Networks, Vol. 5, No. 1, pp.15–23. January, 1994.
Sareni, B.; Krähenbühl, L.:“Fitness sharing and niching methods revisited”. IEEE Trans. on Evolutionary Computation, Vol. 2, No. 3, pp.97–106. September, 1998.
Rivera, A.; Ortega, J.; Prieto A.:”Design of RBF networks by cooperative/competitive evolution of units” International Conference on Artificial Neural Networks and Genetic Algorithms, ICANNGA 2001. April 2001.
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Rivera, A.J., Ortega, J., Rojas, I., Prieto, A. (2001). Optimizing RBF Networks with Cooperative/Competitive Evolution of Units and Fuzzy Rules. In: Mira, J., Prieto, A. (eds) Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence. IWANN 2001. Lecture Notes in Computer Science, vol 2084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45720-8_68
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DOI: https://doi.org/10.1007/3-540-45720-8_68
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