An efficient MDL-based construction of RBF networks

Neural Networks

Volumn 11, Issue 5, 1998, Pages 963-973

  Leonardis, Aleš ^a   Bischof, Horst ^b  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Function approximation; Heart disease classification; Minimum Description Length principle; Optimizing radial basis function network; Radial basis functions

Indexed keywords

ADAPTIVE SYSTEMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; ITERATIVE METHODS; LEARNING SYSTEMS;

FUNCTION APPROXIMATION; HEART DISEASE CLASSIFICATION; MINIMUM DESCRIPTION LENGTH PRINCIPLE; RADIAL BASIS FUNCTION NETWORKS;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; HEART DISEASE; MATHEMATICAL COMPUTING; PRIORITY JOURNAL;

EID: 0032123243     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(98)00051-3     Document Type: Article

References (44)

1. Akaike, H. (1973). Information and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), 2nd International Symposion on Information Theory (pp. 267-281).
2. Bischof H., Leonardis A. Finding optimal neural networks for land use classification. IEEE Transactions on Geoscience and Remote Sensing. 36(1):1998;337-341.
3. Bishop C. M. Curvature-driven smoothing: a learning algorithm for feedforward networks. IEEE Transactions on Neural Networks. 4(5):1993;882-884.
4. Bishop C. M. Training with noise is equivalent to Tikhonov regularization. Neural Computation. 7(1):1995;108-116.
5. Chen D. S., Jain R. C. A robust back propagation learning algorithm for function approximation. IEEE Transactions on Neural Networks. 5(3):1994;467-479.
6. Cichocki, A. & Unbehauen, R. (1993). Neural Networks for Optimization and Signal Processing. New York: Wiley.
7. Fahlman, S. E. & Lebiere, C. (1990). The cascade-correlation learning architecture. In D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems, Vol. 2 (pp. 524-532). Morgan Kaufmann.
8. Fritzke B. Fast learning with incremental RBF networks. Neural Processing Letters. 1(1):1994;2-5.
9. Fua P. & Hanson A.J. (1989). Objective functions for feature discrimination. In Proceedings of the 11th International Joint Conference on Artificial Intelligence, Detroit, MI (pp. 1596-1602). Morgan Kaufmann.
10. Girosi F., Jones M., Poggio T. Regularization theory and neural network architectures. Neural Computation. 7(2):1995;219-269.
11. Glover F. & Laguna M., 1993, Tabu search. In C. R. Reeves (Ed.), Modern Heuristic Techniques for Combinatorial Problems, (pp. 70-150). Blackwell Scientific Publications.
12. Hassibi B. & Stork D. G. (1993). Second order derivatives for network pruning: optimal brain surgeon. In S. J. Hanson et al. (Eds.), NIPS 5, (pp. 164-172). Morgan Kaufmann.
13. Haykin, S. (1994). Neural Networks: A Comprehensive Foundation. New York: McMillan.
14. Hinton G. Connectionist learning procedures. Artificial Intelligence. 40:1989;185-234.
15. Hochreiter S., Schmidhuber J. Flat minima. Neural Computation. 9(1):1997;1-43.
16. Leclerc Y. G. Constructing simple stable descriptions for image partitioning. International Journal of Computer Vision. 3:1989;73-102.
17. Le Cun, Y.L., Denker, J.S. & Solla S.A. (1988). Optimal brain damage. In D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems 2 (pp. 598-605). San Mateo, CA: Morgan Kaufmann.
18. Leonardis, A. & Bischof, H. (1996). Dealing with occlusions in the eigenspace approach. In Proc. of CVPR96 (pp. 453-458). IEEE Computer Society Press.
19. Leonardis A., Gupta A., Bajcsy R. Segmentation of range images as the search for geometric parametric models. International Journal of Computer Vision. 14(3):1995;253-277.
20. Liano K. Robust error measure for supervised neural network learning with outliers. IEEE Transactions on Neural Networks. 7(1):1996;246-250.
21. Lowe D.G. (1989). Adaptive radial basis function nonlinearities, and the problem of generalization. In 1st IEE Conference on Artificial Neural Networks, London, UK (pp. 171-175).
22. MacKay, D. J. C. (1992a) Bayesian interpolation. Neural Computation, 4(3), 415-447.
23. MacKay, D. J. C. (1992b). A practical Bayesian framework for backpropagation networks. Neural Computation, 4(3), 448-472.
24. Moody, J. E. (1992). The effective number of parameters: an analysis of generalization and regularization in nonlinear learning systems. In J. E. Moody, S. J. Hanson & R. P. Lippmann (Eds.), Advances in Neural Information Processing Systems 4 (pp. 847-854). Morgan Kaufmann.
25. Moody J. E., Darken C. Fast learning in networks of locally tuned processing units. Neural Computation. 1(2):1989;281-294.
26. Mozer M. C. & Smolensky P. (1989). Skeletonization: a technique for trimming the fat from a network via relevance assessment. In D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems, Vol. 1 (pp. 107-115). San Mateo, CA: Morgan Kaufmann.
27. Nowlan S. J., Hinton G. E. Simplifying neural networks by soft weight sharing. Neural Computation. 4(4):1992;473-493.
28. Orr M. J. Regularization in the selection of basis function centers. Neural Computation. 7(3):1995;606-623.
29. Pentland A. P. Automatic extraction of deformable part models. International Journal of Computer Vision. 4:1990;107-126.
30. Platt C. J. A resource allocating network for function interpolation. Neural Computation. 3(2):1991;213-225.
31. Poggio T., Girosi F. Networks for approximation and learning. Proceedings of the IEEE. 78(9):1990;1481-1497.
32. Rissanen J. A universal prior for the integers and estimation by minimum description length. Annals of Statistics. 11(2):1983;416-431.
33. Rissanen J. Universal coding, information, prediction, and estimation. IEEE Transactions on Information Theory. 30:1984;629-636.
34. Rissanen, J. (1989). Stochastic Complexity in Statistical Inquiry, Series in Computer Science, Vol. 15. World Scientific.
35. Roy A., Govil S., Miranda R. An algorithm to generate radial basis function (RBF)-like nets for classification problems. Neural Networks. 8(2):1995;179-201.
36. Sardo L. & Kittler J. (1996). Complexity analysis of RBF networks for pattern recognition. In Proceedings of the CVPR'96 (pp. 574-579). IEEE Computer Society Press.
37. Shannon C. A mathematical theory of communication. Bell Systems Technical Journal. 27:1948;379-423.
38. Stone M. Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society B: 36(1):1974;111-147.
39. Stricker, M. & Leonardis, A. (1995). ExSel++: a general framework to extract parametric models. In V. Hlavac & R. Sara (Eds.), 6th CAIP'95, number 970 in Lecture Notes in Computer Science (pp. 90-97), Prague, Czech Republic, 1995. Springer.
40. Vapnik V. N. (1982). Estimation of Dependences Based on Empirical Data. Springer Verlag.
41. Weigend A. S., Huberman B. A., Rumelhart D. E. Predicting the future: a connectionist approach. International Journal of Neural Systems. 1(3):1990;193-209.
42. Whitehead B. A., Choate T. D. Cooperative-competitive genetic evolution of radial basis function centers and widths for time series prediction. IEEE Transactions on Neural Networks. 5(1):1995;15-23.
43. Yingwei L., Sundarajan N., Saratchandran P. A sequential learning scheme for function approximation using minimal radial basis function neural networks. Neural Computation. 9(2):1997;461-478.
44. Zemel R. S., Hinton G. E. Learning population codes by minimum description length. Neural Computation. 7(3):1995;549-564.