A neural-network learning theory and a polynomial time RBF algorithm

IEEE Transactions on Neural Networks

Volumn 8, Issue 6, 1997, Pages 1301-1313

  Roy, Asim ^a,b   Govil, Sandeep ^b   Miranda, Raymond ^b  

^a IEEE   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Designing neural networks; Feedforward nets; Learning complexity; Learning theory; Linear programming; Polynomial time complexity; Radial basis function networks

Indexed keywords

ADAPTIVE ALGORITHMS; APPROXIMATION THEORY; CHAOS THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; FUNCTIONS; LEARNING ALGORITHMS; LEARNING SYSTEMS; LINEAR PROGRAMMING; POLYNOMIALS; PROBLEM SOLVING; TIME SERIES ANALYSIS;

LEARNING COMPLEXITY; POLYNOMIAL TIME COMPLEXITY; RADIAL BASIS FUNCTION ALGORITHM;

FEEDFORWARD NEURAL NETWORKS;

EID: 0031276993     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.641453     Document Type: Article

References (40)

1. Automatic Forecasting Systems, AUTOBOX, Software User Manual, Hatboro, PA, 1988.
2. P. Baldi, "Computing with arrays of bell-shaped and sigmoid functions," in Proc. IEEE Neural Inform. Processing Syst., vol. 3, 1990, pp. 728-734.
3. S. M. Botros and C. G. Atkeson, "Generalization properties of radial basis function," in Advances in Neural Information Processing System, vol. 3, R. P. Lippman, J. E. Moody, and D. S. Touretzky, Eds. San Mateo, CA: Morgan Kaufmann, 1991, pp. 707-713.
4. G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control. San Francisco, CA: Holden-Day, 1976.
5. D. Broomhead and D. Lowe, "Multivariable function interpolation and adaptive networks," Complex Syst., vol. 2, pp. 321-355, 1988.
6. A. L. Blum and R. L. Rivest, "Training a 3-node neural network is NP-complete," Neural Network, vol. 5, no. 1, pp. 117-127, 1992.
7. S. Chen, C. F. N. Cowan, and P. M. Grant, "Orthogonal least squares learning algorithm for radial basis function networks," IEEE Trans. Neural Networks, vol. 2, pp. 302-309, 1991.
8. F. Girosi and T. Poggio, "Networks and the best approximation property," Biol. Cybern., vol. 63, pp. 169-176.
9. F. Glover, "Improved linear programming models for discriminant analysis," Decision Sci., vol. 21, no. 4, pp. 771-785, 1990.
10. E. J. Hartman, J. D. Keeler, and J. M. Kowalski, "Layered neural networks with Gaussian hidden units S universal approximations," Neural Computa., vol. 2, pp. 210-215, 1990.
11. J. S. Judd, Neural Network Design and the Complexity of Learning. Cambridge, MA: MIT Press, 1990.
12. V. Kardirkamanathan, M. Niranjan, and F. Fallside, "Sequential adaptation of radial basis function neural networks and its application to time-series prediction," in Advances in Neural Information Processing System, R. P. Lippmann, J. E. Moddy, and D. S. Touretzky, Eds. San Mateo: Morgan Kaufmann, 1991, vol. 3, pp. 721-727.
13. N. Karmarkar, "A new polynomial time algorithm for linear programming," Combinatorica, vol. 4, pp. 373-395, 1984.
14. L. G. Khachian, "A polynomial algorithm in linear programming," Dorl. Akad. Nauk SSR, vol. 244, no. 5, pp. 1093-1096, 1979.
15. A. Lapedes and R. Farber, "Nonlinear signal processing using neural networks: Prediction and system modeling," Los Alamos Nat. Lab Tech. Rep. LA-UR-87-2262, 1987.
16. S. Makridakis et al., "The accuracy of extrapolation (time series) methods: Results of a forecasting competition," J. Forecasting, vol. 1, pp. 111-153, 1982.
17. O. L. Mangasarian, R. Setiono, and W. H. Wolberg, "Pattern recognition via linear programming: Theory and application to medical diagnosis," in Proc. Wkshp. Large-Scale Numerical Optimization, T. F. Coleman and Y. Li, Eds. Philadelphia, PA: SIAM, 1990, Ithaca, NY: Cornell Univ., Oct. 19-20, 1989, pp. 22-31.
18. R. C. Montiero and I. Adler, "Interior path following primal-dual algorithms. Part I: Linear programming," Math. Programming, vol. 44, pp. 27-41, 1989.
19. M. Minsky and S. Papert, Perceptions. Cambridge, MA: MIT Press, 1988.
20. J. Moody and C. Darken, "Learning with localized receptive fields," in Proc. 1988 Connectionist Models Summer School, D. S. Touretzky, G. E. Hinton, and T. Sejnowski, Eds. San Mateo, CA: Morgan-Kaufmann, 1988, pp. 133-143.
21. _, "Fast learning in networks of locally-tuned processing units," Neural Computa., vol. 1, no. 2, pp. 281-294, 1989.
22. S. Mukhopadhyay, A. Roy, L. S. Kim, and S. Govil, "A polynomial time algorithm for generating neural networks for pattern classification - Its stability properties and some test results," Neural Computa., vol. 5, no. 2, pp. 225-238, 1993.
23. M. T. Musavi, W. Ahmed, K. H. Chan, K. B. Fans, and D. M. Hummels, "On the training of radial basis function classifiers," Neural Networks, vol. 5, no. 4, pp. 595-603, 1992.
24. K. S. Narendra and K. Parthasarathy, "Identification and control of dynamical systems using neural networks," IEEE Trans. Neural Networks, vol. 1, pp. 4-27, 1990.
25. J. Park and I. W. Sandberg, "Universal approximation using radial-basis-fünction networks," Neural Computa., vol. 3, pp. 246-257, 1991.
26. _, "Universal approximation using radial-basis-function networks," Neural Computa., vol. 5, pp. 305-316, 1993.
27. J. Platt, "A resource-allocating network for function interpolation," Neural Computa., vol. 3, no. 2, pp. 213-225, 1991.
28. T. Poggio and F. Girosi, "Regularization algorithms for learning that are equivalent to multilayer networks," Science, vol. 247, pp. 978-982, 1990.
29. M. J. D. Powell, "Radial basis functions for multivariable interpolation: A review," in Algorithms for Approximation, J. C. Mason, M. G. Cox, Eds. Oxford, U.K.: Clarendons, 1987, pp. 143-167.
30. S. Renals and R. Rohwer,"Phoneme classification experiments using radial basis function," in Proc. Int. Joint Conf. Neural Networks, vol. I, 1989, pp. 461-467.
31. A. Roy and S. Mukhopadhyay, "Pattern classification using linear programming," ORSA J. Computing, Winter, vol. 3, no. 1, pp. 66-80, 1991.
32. A. Roy, L. S. Kim, and S. Mukhopadhyay, "A polynomial time algorithm for the construction and training of a class of multilayer perceptrons," Neural Networks, vol. 6, no. 4, pp. 535-545, 1993.
33. A. Roy, S. Govil, and R. Miranda, "An algorithm to generate radial basis function (rbf)-like nets for classification problems," Neural Networks, vol. 8, no. 2, pp. 179-201, 1995.
34. R. Sharda and R. Patil, "Neural networks as forecasting experts: An empirical test," in Proc. Int. Joint Conf. Neural Networks, vol. II, 1990, pp. 491-494.
35. M. Todd and Y. Ye, "A centered projective algorithm for linear programming," Math. Operations Res., vol. 15, no. 3, pp. 508-529, 1990.
36. G. Vrckovnik, C. R. Carter, and S. Haykin, "Radial basis function classification of impulse radar waveforms," in Proc. Int. Joint Conf. Neural Networks, 1990, vol. I, pp. 45-50.
37. N. Weymaere and J. Martens, "A fast robust learning algorithm for feedforward neural networks," Neural Networks, vol. 4, pp. 361-369, 1991.
38. B. Widrow and M. Hoff, "Adaptive switching circuits," in 1960 IRE WESCON Convention Rec., New York, 1960, pp. 96-104.
39. L. Xu, S. Klasa, and A. L. Yuille, "Recent advances on techniques of static feedforward networks with supervised learning," Int. J. Neural Syst., vol. 3, no. 3, pp. 253-290, 1992.
40. L. Xu, A. Krzyzak, and E. Oja, "Rival penalized competitive learning for clustering analysis, rbf net, and curve detection," IEEE Trans. Neural Networks, vol. 4, pp. 636-649, 1993.