Shape-adaptive radial basis functions

IEEE Transactions on Neural Networks

Volumn 9, Issue 6, 1998, Pages 1155-1166

  Webb, Andrew R ^a   Shannon, Simon ^a  

^a DEFENCE SCIENCE AND TECHNOLOGY LABORATORY   (United Kingdom)

Author keywords

Conjugate gradient method; Discriminant analysis; Exploratory data analysis; Neural networks; Nonlinear optimization; Nonlinear transformation; Nonparametric regression; Optimal scaling; Radial basis functions; Statistical pattern recognition

Indexed keywords

ALGORITHMS; DATA REDUCTION; NEURAL NETWORKS; OPTIMIZATION; REGRESSION ANALYSIS;

CONJUGATE GRADIENT METHOD; DISCRIMINANT ANALYSIS; EXPLORATORY DATA ANALYSIS; NONLINEAR OPTIMIZATION; NONLINEAR TRANSFORMATION; NONPARAMETRIC REGRESSION; OPTIMAL SCALING; RADIAL BASIS FUNCTIONS; STATISTICAL PATTERN RECOGNITION;

FUNCTIONS;

EID: 0032208193     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.728359     Document Type: Article

References (33)

1. S. Aeberhard, D. Coomans, and O. de Vel, "Comparative analysis of statistical pattern recognition methods in high-dimensional settings," Pattern Recognition, vol. 27, no. 8, pp. 1065-1077, 1994.
2. L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and Regression Trees. Belmont, CA: Wadsworth, 1984.
3. L. Breiman and J. H. Friedman, "Estimating optimal transformations for multiple regression and correlation," J. Amer. Statist. Assoc., vol. 80, no. 391, pp. 580-619, 1985.
4. L. Breiman and R. Ihaka, "Nonlinear discriminant analysis via scaling and ACE," Dept. Statist., Univ. California, Berkeley, Tech. Rep. 40, 1984.
5. L. Breiman, "Hinging hyperplanes for regression, classification and function approximation," IEEE Trans. Inform. Theory, vol. 39, pp. 999-1013, 1993.
6. D. S. Broomhead and D. Lowe, "Multivariable functional interpolation and adaptive networks," Complex Syst., vol. 2, no. 3, pp. 269-303, 1988.
7. A. Cutler and L. Breiman, "Archetypal analysis," Technometrics, vol. 36, no. 4, pp. 338-347, 1993.
8. J. Duchon, "Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces," R.A.I.R.O. Analyze Numérique, vol. 10, no. 12, pp. 5-12, 1976.
9. J. H. Friedman and W. Stuetzle, "Projection pursuit regression," J. Amer. Statist. Assoc., vol. 76, no. 376, pp. 817-823, 1981.
10. J. H. Friedman, "Multivariate adaptive regression splines," Ann. Statist., vol. 19, no. 1, pp. 1-141, 1991.
11. G. H. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics, vol. 21, pp. 215-223, 1979.
12. P. J. Green and B. W. Silverman, "Nonlinear regression and generalized linear models. A roughness penalty approach," in Monographs on Statistics and Applied Probability, no. 58. London, U.K.: Chapman and Hall, 1994.
13. D. J. Hand, Construction and Assessment of Classification Rules. Chichester, U.K.: Wiley, 1997.
14. D. J. Hand, F. Daley, A. D. Lunn, K. J. McConway, and E. Ostrowski, A Handbook of Small Data Sets. London, U.K.: Chapman and Hall, 1994.
15. J. A. Hartigan and M. A. Wong, "A k-means clustering algorithm," Appl. Statist., vol. 28, pp. 100-110, 1979.
16. T. J. Hastie and R. J. Tibshirani, "Generalized additive models," in Monographs on Statistics and Applied Probability. London, U.K.: Chapman and Hall, 1990.
17. T. J. Hastie, R. Tibshirani, and A. Buja, "Flexible discriminant analysis by optimal scoring," J. Amer. Statist. Assoc., vol. 89, no. 428, pp. 1255-1270, 1994.
18. S. Haykin, Neural Networks. A Comprehensive Foundation. New York: Macmillan, 1994.
19. W. Y. Huang and R. P. Lippmann, "Neural net and traditional classifiers," in Neural Information Processing Systems, D. Z. Anderson, Ed. Amer. Inst. Phys., 1988.
20. P. J. Huber, "Projection pursuit (with discussion)," Ann. Statist., vol. 13, no. 2, pp. 435-525, 1985.
21. M. C. Jones and R. Sibson, "What is projection pursuit (with discussion)," J. Roy. Statist. Soc. A, vol. 150, pp. 1-36, 1987.
22. D. Lowe, "Radial basis functions," in The Handbook of Brain Theory and Neural Networks, M. A. Arbib, Ed. Cambridge, MA: MIT Press, 1995.
23. _, "On the use of nonlocal and non positive definite basis functions in radial basis function networks," in Inst. Elect. Eng. Int. Conf. Artificial Neural Networks, Cambridge, U.K., 1995, pp. 206-211.
24. _, "Characterising complexity in a radial basis function network," in Inst. Elect. Eng. Int. Conf. Artificial Neural Networks, Cambridge, U.K., 1997, pp. 19-23.
25. J. Meinguet, "Multivariate interpolation at arbitrary points made simple," J. Appl. Math. Phys. (ZAMP), vol. 30, pp. 292-304, 1979.
26. J. Park and I. W. Sandberg, "Universal approximation using radial-basisfunction networks," Neural Comput., vol. 3, pp. 246-257, 1991.
27. G. E. Peterson and H. L. Barney, "Control methods used in a study of vowels," J. Acoust. Soc. Amer., vol. 24, pp. 175-184, 1952.
28. D. E. Rumelhart, G. E. Hinton, and R. J. Williams, "Learning internal representation by error propagation," in Parallel Distributed Processing: Explorations in the Microstructure of Cognition. Cambridge, MA: MIT Press, 1986.
29. B. W. Silverman, "Density estimation for statistics and data analysis," in Monographs on Statistics and Applied Probability. London, U.K.: Chapman and Hall, 1986.
30. J. W. Smith, J. E. Everhart, W. C. Dickson, W. C. Knowler, and R. S. Johannes, "Using the ADAP learning algorithm to forecast the onset of diabetes mellitus," in Proc. Symp. Comput. Applicat. Medical Care, 1988, pp. 261-265.
31. G. R. Terrell and D. W. Scott, "Variable kernel density estimation," Ann. Statist., vol. 20, no. 3, pp. 1236-1265, 1992.
32. A. R. Webb, "Functional approximation in feed-forward networks: A least-squares approach to generalization," IEEE Trans. Neural Networks, vol. 5, pp. 363-371, 1994.
33. K. Yu, D. J. Hand, and A. R. Webb, "Evaluating the imprecision of classification rules," submitted, 1997.