Evolving Space-Filling Curves to Distribute Radial Basis Functions Over an Input Space

IEEE Transactions on Neural Networks

Volumn 5, Issue 1, 1994, Pages 15-23

  Whitehead, Bruce A ^a   Choate, Timothy D ^b  

^a UNIVERSITY OF TENNESSEE SPACE INSTITUTE   (United States)

^b ERC Incorporated   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER ARCHITECTURE; ENCODING (SYMBOLS); LEARNING SYSTEMS; OPTIMIZATION; PERFORMANCE; TIME SERIES ANALYSIS;

CLUSTERING; INPUT SPACE; MACKEY-GLASS TIME SERIES; RADIAL BASIS FUNCTION NETWORK; SPACE FILLING CURVE;

NEURAL NETWORKS;

EID: 0028208116     PISSN: 10459227     EISSN: 19410093     Source Type: Journal    
DOI: 10.1109/72.265957     Document Type: Article

References (44)

1. X. Yao, “A review of evolutionary artificial neural networks,” International Journal of Intelligent Systems, vol. 8, no. 4, pp. 539–567, 1993.
2. D. Whitley and T. Hanson, “Optimizing neural networks using faster, more accurate genetic search,” in Proceedings of the Third International Conference on Genetic Algorithms, J. D. Schaffer, Ed. San Mateo, CA: Morgan Kaufmann, June 1989, pp. 391–396.
3. T. P. Caudell and C. P. Dolan, “Parametric connectivity: Training of constrained networks using genetic algorithms,” in Proceedings of the Third International Conference on Genetic Algorithms, J. D. Schaffer, Ed. San Mateo, CA: Morgan Kaufmann, June 1989, pp. 370–374.
4. H. de Garis, “Genetic programming: Building artificial nervous systems using genetically programmed neural network modules,” in Machine Learning: Proceedings of the Seventh International Conference, B. Porter and R. Mooney, Eds. San Mateo, CA: Morgan Kaufmann, June 1990, pp. 132–139.
5. D. J. Montana and L. Davis, “Training feedforward neural networks using genetic algorithms,” in Proceedings of the Eleventh International Joint Conference on Artificial Intelligence. San Mateo, CA: Morgan Kaufmann, August 1989, pp. 762–767.
6. H. Kitano, “Empirical studies on the speed of converengence of neural network training using genetic algorithms,” in Proceedings of the Eighth National Conference on Al (AAAI-90), MIT Press, July-August 1990, 789–795.
7. S. Dominic, R. Das, D. Wrhitley, and C. Anderson, “Genetic reinforcement learning for neural networks,” in IJCNN-91-Seattle: International Joint Conference on Neural Networks, IEEE, July 1991, pp. II-71—II-76.
8. J. R. Koza and J. P. Rice, “Genetic generation of both the weights and architecture for a neural network,” in IJCNN-91-Seattle: International Joint Conference on Neural Networks, IEEE, July 1991, pp. II-397—II-404.
9. G. F. Miller, P. M. Todd, and S. U. Hegde, “Designing neural networks using genetic algorithms,” in Proceedings of the Third International Conference on Genetic Algorithms, J. D. Schaffer, Ed. San Mateo, CA: Morgan Kaufmann, June 1989, 379–384.
10. J. D. Schaffer, R. A. Caruana, and L. J. Eshelman, “Using genetic search to exploit the emergent behavior of neural networks,” in Emergent Computation: Self-organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks, S. Forrest, Ed. Cambridge, MA: MIT Press, 1990, 244–248.
11. S. W. Wilson, “Perceptron redux: Emergence of structure,” in Emergent Computation: Self-Organizing, Collective, and Cooperative Phenomena in Natural and Artificial Computing Networks, S. Forrest, Ed. Cam-bridge, MA: The MIT Press, 1990, pp. 249–256.
12. S. Bomholdt and D. Graudenz, “General asymmetric neural networks and structure design by genetic algorithms,” Neural Networks, vol. 5, no. 1, pp. 327–334, 1992.
13. S. A. Harp, T. Samad, and A. Guha, “Designing application-specific neural networks using the genetic algorithms,” in Advances in neural Information Processing Systems 2, D. S. Touretzky, Ed. San Mateo, CA: Morgan Kaufmann, 1990, pp. 447–454.
14. S. A. Harp and T. Samad, “Genetic optimization of self-organizing feature maps,” in IJCNN-91-Seattle: International Joint Conference on Neural Networks, IEEE, July 1991, pp. I-341-I-346.
15. S. A. Harp, T. Samad and A. Guha, “Towards the genetic synthesis of neural networks,” in Proceedings of the Third International Conference on Genetic Algorithms, J.D. Schaffer, Ed. San Mateo, CA: Morgan Kaufmann, June 1989, pp. 360–369.
16. H. Kitano, “Designing neural networks using genetic algorithms with system,” Complex Systems, vol. 4, 461–476, 1990.
17. J. W. L. Merrill and R. F. Port, “Fractally configured neural networks,” Neural Networks, vol. 4, pp. 53–60, 1991.
18. D. B. Fogel, L. J. Fogel, and V. W. Porto, “Evolving neural networks,” Biological Cybernetics, vol. 63, pp. 487–493, 1990.
19. H. Barun and J. Weisbrod, “Evolving neural networks for application oriented problems,” in Proceedings of 2nd Annual Conference on Evolutionary Programming, D. B. Fogel and W. Atmar, Eds. La Jolla, CA: Evolutionary Programming Society, 1993, 62–71.
20. D. B. Fogel, “Using evolutionary programming to create neural networks that are capable of playing tic-tac-toe,” in International Conference on Neural Networks, 1993, pp. 875–880.
21. J. R. McDonnell and D. Waagen, “Neural network structure design by evolutionary programming,” in Proceedings of 2nd Annual Conference on Evolutionary Programming, D.B. Fogel and W. Atmar, Eds. La Jolla, CA: Evolutionary Programming Society, 1993, pp. 79–89.
22. M. J. D. Powell, “Radial basis functions for multivariable interpolation: A review,” in IMA Conference on Algorithms for the Approximation of Functions and Data, J. C. Mason and M. G. Cox, Eds. Royal Military College of Science: Oxford University Press, 1987, pp. 143–167.
23. D. S. Broomhead and D. Lowe, “Multivariable functional interpolation and adaptive networks,” Complex Systems, vol. 2, pp. 321–355, 1988.
24. M. J. D. Powell, “The theory of radial basis function approximation in 1990, volume II,” in Advances in Numerical Analysis, W. Light, Ed. Oxford: Clarendon Press, 1992, pp. 105–210.
25. J. Moody and C. J. Darken, “Fast learning in networks of locally-tuned processing units,” Neural Computation, vol. 1, pp. 281–294, 1989.
26. T. Poggio and F. Girosi, “Networks for approximation and learning,” Proceedings of the IEEE, vol. 78, no. 9, 1990, pp. 1481–1497.
27. F. Girosi, “Some extensions of radial basis functions and their applications in artificial intelligence,” Computers Math Applic., vol. 24, no. 12, pp. 61–80, 1992.
28. C. Bishop, “Improving the generalization properties of radial basis function neural networks,” Neural Computation, vol. 3, no. 4, pp. 579–588, 1991.
29. B. Widrow and M. E. Hoff, “Adaptive switching circuits,” in 1960 WESCON Convention, 1960, pp. 96–104.
30. M. T. Musavi, W. Ahmed, K. H. Chan, K. B. Faris, and D. M. Hummels, “On the training of radial basis function classifiers,” Neural Networks, vol. 5, 595–603, 1992.
31. J. H. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor, MI: The University of Michigan Press, 1975.
32. D. Whitely, “The genitor algorithm and selection pressure: Why rank-based allocation of reproductive trials is best,” in Proceedings of the Third International Conference on Genetic Algorithms. San Mateo, CA: Morgan Kaufmann, June 1989, pp. 116–121.
33. E. A. Patrick, D. R. Anderson, and F. K. Bechtel, “Mapping multidimensional space to one dimension for csamtomputer output display,” IEEE Transactions on Computers, vol. C-17, no. 10, pp. 949–953, 1968.
34. D. E. Goldberg, “Real-coded genetic algorithms, virtual alphabets, and blocking,” Complex Systems, vol. 5, pp. 139–167, 1991.
35. M. C. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science, vol. 197, pp. 287–289, 1977.
36. A. Lapedes and R. Farber, “How neural nets work,” in Neural Information Processing Systems. New York: American Institute of Physics, 1988, pp. 442–456.
37. J. D. Farmer and J. H. Sidorowich, “Predicting chaotic time series,” Physical Review Letters, vol. 59, no. 8, pp. 845–848, 1987.
38. M. F. Tenorio, “Self-organizing network for optimum supervised learning,” IEEE Transactions on Neural Networks, vol. 1, no. 1, pp. 100–110, 1990.
39. J. Platt, “A resource-allocating network for function interpolation,” Neural vol. 3, 213–225, 1991.
40. E. Hartman and J. D. Keeler, “Predicting the future: Advantages of semilocal units,” Neural Computation, vol. 3, pp. 566–578, 1991.
41. S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Transactions on Neural Networks, vol. 2, no. 2, pp. 302–309, 1991.
42. T. Kohonen, “An introduction to neural computing,” Neural Networks, vol. 1, no. 1, pp. 3–16, 1988.
43. T. A. Foley, “The map and blend scattered data interpolant on a sphere,” Computers Math. Applic., vol. 24, no. 12, pp. 49–60, 1992.
44. K. Salkauskas, “Moving least squares interpolation with thin-plate splines and radial basis functions,” Computers Math. Applic., vol. 24, no. 12, pp. 177–185, 1992.