Function Approximation with Radial Basis Function Neural Networks via FIR Filter
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.
[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.
[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.
@article{"International Journal of Information, Control and Computer Sciences:65716", author = "Kyu Chul Lee and Sung Hyun Yoo and Choon Ki Ahn and Myo Taeg Lim", title = "Function Approximation with Radial Basis Function Neural Networks via FIR Filter", 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.", volume = "8", number = "8", pages = "1386-4", }
