Construction of classifiers based on kernel density estimations using the a posteriori probabilities of competing sets

1Anisimov, AV
1Galkin, OA
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2015, 9:25-32
Section: Information Science and Cybernetics
Language: Ukrainian

An approach is proposed to construct classifiers based on kernel density estimates for solving pattern recognition problems. The approach is based on the use of the a posteriori probability and a distributive π-type measure for the effective division of competing sets. The family of density estimates is applied to each set in a wide range of bandwidths for each estimate of the class density. A procedure is proposed and adapted to combine the classification results on different levels of smoothing that provides a flexible use of different bandwidths for different pairs of competing classes. Statistical uncertainties are calculated on the basis of approximate estimated probabilities of a misclassification.

Keywords: classification rule, density estimate, weight function
  1. Godtliebsen F., Marron J. S., Chaudhuri P. J. of Computational and Graphical Statistics, 2002, 11: 3–21.
  2. Holmes C. C., Adams N. M. J. of the Royal Statistical Society, 2002, 64: 297–304.
  3. Hall P. The Annals of Statistics, 1983, 11: 1160–1173.
  4. Lachenbruch P., Mickey M. Technometrics, 1968, 10: 3–10.
  5. Silverman B. W. Density estimation for Statistics and Data Analysis, London: Chapman and Hall, 1986.
  6. Wand M., Jones M. Kernel Smoothing, London: Chapman and Hall, 1995: 1–14.
  7. Ripley B. Pattern Recognition and Neural Networks, Cambridge: Cambridge University Press, 1996: 1–17.
  8. Duda R., Hart P., Stork D. Pattern Classification, New York: Wiley, 2000: 1–21.
  9. Chaudhuri P., Marron J. The Annals of Statistics, 2000, 28: 410–427.