A fast procedure is proposed for choosing the blur coefficients of kernel functions in a multidimensional nonparametric estimation of the equation of a decision surface for a two-alternative problem of pattern recognition. The decision classification rule meets the maximum likelihood criterion. The theoretical basis of the procedure under consideration is the result of a study of the asymptotic properties of multidimensional nonparametric estimates of the decision function in the problem of recognizing patterns and probability densities of the distribution of random variables in classes. The possibility of using fast procedures for choosing the blur coefficients of kernel estimates of probability densities in the synthesis of non-parametric estimates of the equation of the decision surface between classes is substantiated. The effectiveness of the proposed approach is confirmed by the results of computational experiments.
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References
A. V. Lapko and V. A. Lapko, “Nonparametric algorithms for estimating the state of natural objects,” Avtometriya, 54, No. 5, 33–39 (2018), DOI: https://doi.org/10.15372/AUT20180504.
I. V. Zenkov, S. T. Im, A. V. Lapko, et al., Development and Application of Information Technologies for the Study of the Natural Resources of Siberian Territories Based on Remote Sensing Data, SibGAU, Krasnoyarsk (2017).
M. I. Borrajo, W. González-Manteiga, and M. D. Martínez-Miranda, “Bandwidth selection for kernel density estimation with length-biased data,” J. Nonparam. Stat., 29, No. 3, 636–668 (2017).
S. Chen, “Optimal bandwidth selection for kernel density functionals estimation,” J. Probab. Stat., 2015, 1–21 (2015).
D. W. Scott, Multivariate Density Estimation: Theory, Practice, and Visualization, John Wiley & Sons, New Jersey (2015).
S. J. Sheather, “Density estimation,” Stat. Sci., 19, No. 4, 588–597 (2004).
B. W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London (1986).
A. V. Lapko and V. A. Lapko, “Fast algorithm for choosing the blur coefficients of kernel functions in a non-parametric estimate of probability density,” Izmer. Tekhn., No. 6, 16–20 (2018), DOI: https://doi.org/10.32446/0368-1025it-2018-6-16-20.
A. V. Lapko and V. A. Lapko, “Fast algorithm for choosing blur coefficients in multidimensional kernel probability density estimates,” Izmer. Tekhn., No. 10, 19–23 (2018), DOI: https://doi.org/10.32446/0368-1025it.2018-10-19-23.
A. V. Lapko and V. A. Lapko, “Technique for fast selection of the blur coefficients of kernel functions in a nonparametric pattern recognition algorithm,” Izmer. Tekhn., No. 4, 4–8 (2019), DOI: https://doi.org/10.32446/0368-1025it.2019-4-4-8.
E. Parzen, “On estimation of a probability density function and mode,” Ann. Math. Stat., 33, No. 3, 1065–1076 (1962).
V. A. Epanechnikov, “Nonparametric estimation of multidimensional probability density,” Teor. Veroyatn. Primen., 14, No. 1, 156–161 (1969).
A. V. Lapko and V. A. Lapko, “Analysis of the asymptotic properties of a nonparametric estimate of the equation of a decision surface in a two-alternative problem of pattern recognition,” Avtometriya, 46, No. 3, 48–53 (2010).
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Translated from Izmeritel’naya Tekhnika, No. 8, pp. 8–13, August, 2019.
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Lapko, A.V., Lapko, V.A. Fast Selection of Blur Coefficients in a Multidimensional Nonparametric Pattern Recognition Algorithm. Meas Tech 62, 665–672 (2019). https://doi.org/10.1007/s11018-019-01676-0
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DOI: https://doi.org/10.1007/s11018-019-01676-0