Function Approximation with Radial Basis Function Neural Networks via FIR Filter

Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

Abstract:

Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation.

Keywords: Extended kalmin filter (EKF), classification problem, radial basis function networks (RBFN), finite impulse response (FIR)filter.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094497

References:

[1] D. S. Broomhead and D. Lowe, ”Multi-variable functional interpolation and adaptive networks,” Complex Systems, vol. 2, pp. 321-355, 1988.
[2] C. A. Miehelli, ”Interpolation of scattered data: distance matrices and conditionally positive definite functionsConstructive Approximation,” 1986.
[3] M. J. D. Powell, ”Radial basis functions for multivariate interpolation,” a review, In J.C. Mason and M.G. Cox, editors, Algorithms for Approximation, Clarendon Press, Oxford, 1987.
[4] V.D. Sanchez, A. (Ed.), ”Special Issue on RBF Networks, Part I,” Neurocomputing 19, 1998.
[5] V.D. Sanchez, A. (Ed.), ”Special Issue on RBF Networks, Part II,” Neurocomputing 20, 1998.
[6] Chen S, Cowan CFN, Grant PM, ”Orthogonal Least Square Learning Algorithm for Radial Basis Function Networks,” IEEE Transactions on Neural Networks, 1991.
[7] D simon, ”Training radial basis neural networks with the extended Kalman filter,” Neurocomputing 48, 2002.
[8] M.T. Musavi, W. Ahmed, K.H. Chan, K.B. Faris, D.M. Hummels, ”On the Training of Radial Basis Function Classifiers”, Neural Networks 5, 1992.
[9] Bernhard Scholkopf, Kah-Kay Sung, Christopher JC Burges, Federico Girosi, Partha Niyogi, Tomaso Poggio, Vladimir Vapnik, ”Comparing support vector machines with Gaussian kernels to radial basis function classifiers,” Signal Processing, IEEE Transactions on, 1997.
[10] D. Broomhead, D. Lowe ”Multivariable functional interpolation and adaptive networks,” Complex Systems 2, 321-355, 1988.
[11] S. Shah, F. Palmieri, M. Datum, ”Optimal filtering algorithms for fast learning in feedforward neural networks,” Neural Networks 5, 779-787, 1992.
[12] J. Sum, C. Leung, G. Young, W. Kan, ”On the Kalman filtering method in neural network training and pruning,” IEEE Trans. Neural Networks 10, 161-166, 1999.
[13] Y. Zhang, X. Li, ”A fast U-D factorization-based learning algorithm with applications to nonlinear system modeling and identification,” IEEE Trans. Neural Networks 10, 930-938, 1999.
[14] D. Obradovic, ”On-line training of recurrent neural networks with continuous topology adaptation,” IEEE Trans. Neural Networks 7 , 222- 228, 1996.
[15] G. Puskorius, L. Feldkamp, ”Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks,” IEEE Trans. Neural Networks 5 (1994) 279-297.
[16] W. H. Kwon and S. Han, ”Receding Horizon Control,” London, U.K., Springer-Verlag, 2005.
[17] Choon Ki Ahn, Soo Hee Han, and Wook Hyun Kwon, ”H FIR Filters for Linear Continuous-time State-space Systems,” IEEE Signal Processing Letters, Vol. 13, No. 9, September, 2006.
[18] Choon Ki Ahn, ”A New Solution to Induced l Finite Impulse Response Filtering Problem Based on Two Matrix Inequalities” International Journal of Control, Taylor & Francis, Volume 87, Issue 2, 2014, pages 404- 409.
[19] Choon Ki Ahn, ”Strictly Passive FIR Filtering for State-space Models with External Disturbance,” International Journal of Electronics and Communications, Elsevier, Volume 66, Issue 11, November 2012, Pages 944-948.
[20] Choon Ki Ahn, Soo Hee Han, andWook Hyun Kwon, ”H Finite Memory Controls for Linear Discrete-time State-space Models,” IEEE Transactions on Circuits & Systems II, Vol. 54, No. 2, February, 2007.
[21] Hyun Duck Choi, Choon Ki Ahn, Myo Taeg Lim, ”Time-domain Filtering for Estimation of Linear Systems with Colored Noises using Recent Finite Measurements,” Measurement, Elsevier, Volume 46, Issue 8, October 2013, Pages 2792-2797.
[22] Choon Ki Ahn, ”Robustness Bound for Receding Horizon Finite Memory Control: Lyapunov-Krasovskii Approach,” International Journal of Control, Taylor & Francis, Volume 85, Issue 7, 2012, pages 942-949.