Nonlinear optimization of RBF networks

International Journal of Systems Science

Volumn 29, Issue 2, 1998, Pages 179-189

  Mcloone, Seán ^a   Irwin, George ^a  

^a QUEEN'S UNIVERSITY BELFAST   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FUNCTIONS; OPTIMIZATION;

RADIAL BASIS FUNCTION (RBF) NETWORKS;

CONTROL THEORY;

EID: 0031999666     PISSN: 00207721     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207729808929510     Document Type: Article

References (29)

1. BATTITI R., 1992, first-and second-order methods for learning: between steepest descent and Newton's method. Neural Computation, 4, 141-166.
2. BISHOP, C. M., 1990, Curvature-driven smoothing in backpropagation neutral networks. Proc. Int. Neutral Networks Conf. 90, pp. 749-753.
3. BOSSLEY, K. M., 1997, Neurofuzzy modelling approaches in system identification. PhD thesis, Department of Electronics and Computer Science, University of Southampton.
4. BROOMHEAD, D. S., and LOWE, D., 1988, Multivariable functional interpolation and adaptive networks. Complex Systems, 2, 321-355.
5. BUHMANN, M. D., and POWELL, M. J. D., 1990, Radial basis function interpolation on an infinite regular grid. Algorithms for Approximation, Vol. 2, edited by J. C. Mason and M. G. Cox (London: Chapman & Hall), pp. 146-169.
6. CHEN, C. L., CHEN, W. C., and CHANG, F. Y., 1993, Hybrid learning algorithm for Gaussian potential function networks. IEE Proc. D, 140, 442-448.
7. CHEN, T., and CHEN, H., 1995, Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks. IEEE Transactions on Neural Networks, 6, 904-910.
8. CHEN, S., COWAN, C. F., and GRANT, P. M., 1991, Orthogonal least squares learning algorithm for radial basis function networks. IEEE Transactions on Neural Networks, 2, 302-309.
9. DRUCKER, H., and LE CUN, Y., 1992, Improving generalization performance using double backpropagation. IEEE Transactions on Neural Networks, 3, 991-997.
10. FAHLMAN, S. E., and LEBIERE, C., 1989, The cascade-correlation architecture. Advances in Neural Information Processing Systems, Vol. 2, edited by D. S. Touretzky (San Mateo, CA: Morgan Kaufmann), pp. 524-532.
11. FLETCHER, R., 1987, Practical Methods of Optimization (Wiley).
12. GILL, P. E., MURRAY, W., and WRIGHT, M. H., 1981, Practical Optimization (Academic Press).
13. GIROSI, F., and POGGIO, T., 1990, Neural networks and the best approximation property. Biological Cybernetics, 63, 169-176.
14. HARTMANN, E. J., KEELER, J. D., and KOWALSKI, J. M., 1990, Layered neural networks with Gaussian hidden units as universal approxirnators. Neural Computation, 2, 210-215.
15. LE CUN, Y., DENKER, J. S., and SOLLA, S. A., 1989, Optimal brain damage. Advances in Neural Information Processing Systems, Vol. 2, edited by D. S. Touretzky (San Mateo, CA: Morgan Kaufmann), pp. 598-605.
16. LIU, B., and SI, J., 1993, The best approximation properties and error bounds of Gaussian networks, Proceedings of the 32nd Conference on Decision and Control, San Antonio, TX, pp. 2798-2803.
17. LOWE, D., 1989, Adaptive radial basis function nonlinearities and the problem of generalisation. 1st IEE International Conference on Artificial Neural Networks, 313, pp. 171-175.
18. MASON, J. C., and PARKS, P. C., 1992, Selection of neural network structures: some approximation theory guidelines. Neural Networks for Control and Systems, edited by K. Warwick, G. W. Irwin and K. J. Hunt (Peter Peregrinus), pp. 151-180.
19. MCKEOWN, J., MEEGAN, D., and SPREVAK, D., 1990, An Introduction to Unconstrained Optimization (Adam Hilger).
20. MCLOONE, S., and IRWIN, G. W., 1995, Fast gradient based off-line training of multilayer perceptrons. Neural Network Engineering in Dynamic Control Systems, edited by K. J. Hunt, G. W. Irwin and K. Warwick (Springer-Verlag), pp. 179-200.
21. MØLLER, M. F., 1993, Efficient training of feed-forward neural networks. PhD thesis, Computer Science Dept, Aarhus University, Denmark.
22. POTTMANN, M., and SEBORG, D. E., 1993, A radial basis function control strategy and its application to a pH neutralisation process. European Control Conference 1993, pp. 2329-2333.
23. POWELL, M. J. D., 1987, radial basis functions for multivariate interpolation'. In Algorithms for Approximation, edited by J. C. Mason and M. G. Cox (Clarendon Press), pp. 143-168.
24. RUMELHART, D. E., HINTON, G. E., and WILLIAMS, R. J., 1986, Learning internal representations by error propagation. Parallel Distributed Processing: Explorations in the Microstructure of Cognition, edited by D. E. Rumelhart and J. L. McClelland, Vol. 1, Chapter 8 (Cambridge, MA: MIT Press).
25. SANNER, R. M., and SLOTINE, J. J. E., 1992, Gaussian networks for direct adaptive control. IEEE Trans. Neural Networks, 3, 837-863.
26. SJÖBERG, J., 1995, Non-linear system identification with neural networks. PhD thesis, Dept. Electrical Engineering, Linkoping University, Sweden.
27. SJÖBERG, J., and LJUNG, L., 1995, Overtraining, regularization, and searching for minimum with application to neural networks. Int. J. Control, 62, 1391-1407.
28. WEBB, A. R., LOWE, D., and BEDWORTH, M. D., 1988, A comparison of nonlinear optimization strategies for feed-forward adaptive layered networks. Royal Signals and Radar Establishment, Memorandum 4157 (London: Controller HMSO).
29. XIAOSONG, D., POPOVIC, D., and SCHULTZ-EKLOFF, G., 1995, Oscillation-resisting in the learning of backpropagation neural networks. 3rd IFAC/IFIP Workshop on Algorithms and Architectures for Real-time Control, Belgium, pp. 21-25.