Abstract
Assuming uniform losses, Bayesian classification leads to the lowest possible misclassification rate, by definition. In order to carry out supervised classification in the Bayes sense, kernel density estimators with variable width are utilized. Nevertheless, in their standard form, they would require each learnt pattern to be stored, which is often beyond the hardware specifications. For this reason the variable kernel algorithm proposed is based on clusters, determined so as to minimize the final misclassification rate. This rate is evaluated by a cross-validation type algorithm in order to avoid overfitting. Experimental results show that it is possible to determine the number of clusters and their parameters, and to take into account hardware constraints, unavoidable in neural implementations.
Part of this work has been funded by the ESPRIT-BRA project 6891, supported by the Commision of the European Communities.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
L. BREIMAN, W. MEISEL, E. PURCELL, “Variable kernel estimates of multivariate densities”, Technometrics, vol. 19, no. 2, pp. 135–144, May 1977.
T. CACOULLOS, “Estimation of a multivariate density”, Annals of Inst. Stat. Math., vol. 18, pp. 178–189, 1966.
P. COMON, “Supervised classification, a probabilistic approach”, in ESANN-European Symposium on Artificial Neural Networks, Verleysen, Ed., Brussels, Apr 19–21 1995, D facto Publ.
P. COMON, C. JUTTEN et al., “ELENA, Axis A: Theory”, Esprit Basic Research Project 6891, CEC, June 1993.
P. COMON, J. L. VOZ, M. VERLEYSEN, “Estimation of performance bounds in supervised classification”, in ESANN-European Symposium on Artificial Neural Networks, M. Verleysen, Ed., April 20–22 1994, pp. 37–42, D facto Publ.
E. DIDAY, “The dynamic clusters method in non hierachical clustering”, Int. Jour. Computer Inf. Sciences, vol. 2, pp. 61–88, 1973.
R.O. DUDA, P.E. HART, Pattern Classification and Scene Analysis, Wiley, 1973.
K. FUKUNAGA, R.R. HAYES, “Estimation of classifier performance”, IEEE Trans. PAMI, vol. 11, no. 10, pp. 1087–1101, Oct. 1989.
D.J. HAND, Kernel Discriminant Analysis, RSP press, 1982.
E. PARZEN, “On the estimation of a probability density function and the mode”, Ann. Math. Stat., vol. 33, pp. 1065–1076, 1962.
T. J. WAGNER, “Nonparametric estimates of probability densities”, IEEE Trans. on Inf. Theory, vol. 21, no. 4, pp. 438–440, July 1975.
Y. CHENEVAL, “Packlib, an interactive environment to develop modular software for data processing”, to appear in IWANN-International Workshop on Artificial Neural Networks, Mira, Ed., Madrid, Jun 7–9 1995, Springer-Verlag.
J.A. NELDER, R. MEAD, “A simplex method for function minimization”, in Comput. J., vol. 5, pp 308–313, 1965
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Comon, P., Cheneval, Y. (1995). Supervised classification with variable kernel estimators. In: Mira, J., Sandoval, F. (eds) From Natural to Artificial Neural Computation. IWANN 1995. Lecture Notes in Computer Science, vol 930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59497-3_290
Download citation
DOI: https://doi.org/10.1007/3-540-59497-3_290
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59497-0
Online ISBN: 978-3-540-49288-7
eBook Packages: Springer Book Archive