Kernel Ho-Kashyap classifier with generalization control

Jacek Łęski

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 1, page 53-61
  • ISSN: 1641-876X

Abstract

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This paper introduces a new classifier design method based on a kernel extension of the classical Ho-Kashyap procedure. The proposed method uses an approximation of the absolute error rather than the squared error to design a classifier, which leads to robustness against outliers and a better approximation of the misclassification error. Additionally, easy control of the generalization ability is obtained using the structural risk minimization induction principle from statistical learning theory. Finally, examples are given to demonstrate the validity of the introduced method.

How to cite

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Łęski, Jacek. "Kernel Ho-Kashyap classifier with generalization control." International Journal of Applied Mathematics and Computer Science 14.1 (2004): 53-61. <http://eudml.org/doc/207678>.

@article{Łęski2004,
abstract = {This paper introduces a new classifier design method based on a kernel extension of the classical Ho-Kashyap procedure. The proposed method uses an approximation of the absolute error rather than the squared error to design a classifier, which leads to robustness against outliers and a better approximation of the misclassification error. Additionally, easy control of the generalization ability is obtained using the structural risk minimization induction principle from statistical learning theory. Finally, examples are given to demonstrate the validity of the introduced method.},
author = {Łęski, Jacek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {classifier design; Ho-Kashyap classifier; kernel methods; robust methods; generalization control},
language = {eng},
number = {1},
pages = {53-61},
title = {Kernel Ho-Kashyap classifier with generalization control},
url = {http://eudml.org/doc/207678},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Łęski, Jacek
TI - Kernel Ho-Kashyap classifier with generalization control
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 1
SP - 53
EP - 61
AB - This paper introduces a new classifier design method based on a kernel extension of the classical Ho-Kashyap procedure. The proposed method uses an approximation of the absolute error rather than the squared error to design a classifier, which leads to robustness against outliers and a better approximation of the misclassification error. Additionally, easy control of the generalization ability is obtained using the structural risk minimization induction principle from statistical learning theory. Finally, examples are given to demonstrate the validity of the introduced method.
LA - eng
KW - classifier design; Ho-Kashyap classifier; kernel methods; robust methods; generalization control
UR - http://eudml.org/doc/207678
ER -

References

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  1. Baudat G. and Anouar F. (2000): Generalized discriminant analysis using a kernel approach. - Neural Comput., Vol. 12, No. 10, pp. 2385-2404. 
  2. Boser B.E., Guyon I.M. and Vapnik V. (1992): A training algorithm for optimal margin classifiers. - Proc. 5th Ann. ACM Workshop Computational Learning Theory, Pittsburgh, USA, pp. 144-152. 
  3. Czogała E. and Łęski J.M. (2000): Fuzzy and Neuro-Fuzzy Intelligent Systems. - Heidelberg: Physica-Verlag. Zbl0953.68122
  4. Duda R.O. and Hart P.E. (1973): Pattern Classification and Scene Analysis. - New York: Wiley. Zbl0277.68056
  5. Gantmacher F.R. (1959): The Theory of Matrices. -New York: Chelsea Publ. Zbl0085.01001
  6. Haykin S. (1999): Neural Networks. A Comprehensive Foundation. - Upper Saddle River: Prentice-Hall. Zbl0934.68076
  7. Ho Y.-C. and Kashyap R.L. (1965): An algorithm for linear inequalities and its applications. - IEEE Trans. Elec. Comp., Vol. 14, No. 5, pp. 683-688. Zbl0173.17902
  8. Ho Y.-C. and Kashyap R.L. (1966): A class of iterative procedures for linear inequalities. - SIAM J. Control., Vol. 4, No. 2, pp. 112-115. Zbl0143.37503
  9. Huber P.J. (1981): Robust Statistics. - New York: Wiley. Zbl0536.62025
  10. Łęski J.M. (2003a): Ho-Kashyap classifier with generalization control. - Pattern Recogn. Lett., Vol. 24, No. 2, pp. 2281-2290. Zbl1047.68128

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