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Function Approximation Using Robust Radial Basis Function Networks
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Journal of Intelligent Learning Systems and Applications·Volume 03 (2011)·Pages 17–25·Published 24 February 2011·DOI10.4236/jilsa.2011.31003
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Abstract
Resistant training in radial basis function (RBF) networks is the topic of this paper. In this paper, one modification of Gauss-Newton training algorithm based on the theory of robust regression for dealing with outliers in the framework of function approximation, system identification and control is proposed. This modification combines the numerical ro- bustness of a particular class of non-quadratic estimators known as M-estimators in Statistics and dead-zone. The al- gorithms is tested on some examples, and the results show that the proposed algorithm not only eliminates the influence of the outliers but has better convergence rate then the standard Gauss-Newton algorithm.
KeywordsNeural NetworkRobust TrainingBasis FunctionDead Zone
- B. Kosko, “Neural Network for Signal Processing,” Pren-tice-Hall Inc., New York, 1992.
- S. Haykin, “Neural Net-works. A Comprehensive Founda- tion,” 2nd Edition, Prentice Hall Inc., New York, 1999.
- C. M. Bishop, “Neural Net-work for Pattern Recognition,” Clarendon Press, Oxford, 1995.
- H. Wang, G. P. Liu, C. J. Harris and M. Brown, “Advanced Adaptive Control,” Pergamon, Oxford, 1995.
- R. Hecht-Nielsen, “Kolmogorov’s Mapping Neural Net- works Existence Theorem,” First IEEE International Conference on Neural Networks, San Diego, Vol. 3, 1987, pp. 11-14.
- G. Cybenko, “Approximation by Superpositions of a Sigmoidal Function,” Mathematics of Control, Signals and Systems, Vol. 2, No. 4, 1989, pp. 303-314. doi:10. 1007/BF02551274
- T. Poggio and F. Girosi, “Networks for Approximation and Learning,” Proceeding of the IEEE, Vol. 78, No. 9, 1990, pp. 1481-1497. doi:10.1109/5.58326
- J. Park and I. W. Sandberg, “Universal Approximation Using Radial-Basis-Function Network,” Neural Compu- tation, Vol. 3, No. 2, 1991, pp. 246-257. doi:10.1162/ne-co.1991.3.2.246
- C. C. de Wit and J. Carrillo, “A Modified EW-RLS Algorithms for Systems with Bounded Disturbances,” Automatica, Vol. 26, No. 3, 1990, pp. 599-606. doi:10.1016/0005-1098(90)90032-D
- P. J. Huber, “Robust Statistics,” John Wiley, New York, 1981. doi:10.1002/0471725250
- R. E. Frank, M. Hampel, M. Rohchetti and W. A. Stanel, “Robust Statistics: The Approach Based on Influence Functions,” John Wiley & Sons Inc., Hoboken, 1986.
- C. C. Chang, J. T. Jeng and P. T. Lin, “Annealing Robust Radial Basis Function Networks for Function Approxi- mation with Outliers,” Neu-rocomputing, Vol. 56, 2004, pp. 123-139. doi:10.1016/S0925-2312(03)00436-3
- S.-C. Chan and Y.-X. Zou, “A Recursive Least M-Esimate Algorithm for Robust Filtering in Impulsive Noise: Fast Algorithm and Convergence Performance Analysis,” IEEE Transactions on Signal Processing, Vol. 52, No. 4, 2004, pp. 975-991. doi:10.1109/TSP.2004.823496
- D. S. Pham and A. M. Zoubir, “A Sequential Algorithm for Robust Parameter Estima-tion,” IEEE Signal Proce- ssing Letters, Vol. 12, No. 1, 2005, pp. 21-24. doi:10.1109/LSP.2004.839689
- J. Ni and Q. Soug, “Pruning Based Robust Backpropaga- tion Training Al-gorithm for RBF Network Training Con- troller,” Intelligent and Robotic Systems, Vol. 48, No. 3, 2007, pp. 375-396. doi:10.1007/s10846-006-9093-x