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Nonparametric pattern recognition algorithm for testing a hypothesis of the independence of random variables
I.V. Zenkov 1,3, A.V. Lapko 2,3, V.A. Lapko 2,3, E.V. Kiryushina 1, V.N. Vokin 1

1 Siberian Federal University,
660041, Krasnoyarsk, Russia, Svobodny Av. 79,
2 Institute of Computational Modelling SB RAS,
660036, Krasnoyarsk, Russia, Akademgorodok 50,
3 Reshetnev Siberian State University of Science and Technology,
660037, Krasnoyarsk, Russia, Krasnoyarsky Rabochy Av. 31

 PDF, 777 kB

DOI: 10.18287/2412-6179-CO-871

Pages: 767-772.

Full text of article: Russian language.

Abstract:
A new method for testing a hypothesis of the independence of multidimensional random variables is proposed. The technique under consideration is based on the use of a nonparametric pattern recognition algorithm that meets a maximum likelihood criterion. In contrast to the traditional formulation of the pattern recognition problem, there is no a priori training sample. The initial information is represented by statistical data, which are made up of the values of a multivariate random variable. The distribution laws of random variables in the classes are estimated according to the initial statistical data for the conditions of their dependence and independence. When selecting optimal bandwidths for nonparametric kernel-type probability density estimates, the minimum standard deviation is used as a criterion. Estimates of the probability of pattern recognition error in the classes are calculated. Based on the minimum value of the estimates of the probabilities of pattern recognition errors, a decision is made on the independence or dependence of the random variables. The technique developed is used in the spectral analysis of remote sensing data.

Keywords:
testing a hypothesis of the independence of random variables, multidimensional random variables, pattern recognition, nonparametric probability density estimation, bandwidths of kernel functions, Kolmogorov–Smirnov criterion, spectral analysis of remote sensing data.

Citation:
Zenkov IV, Lapko AV, Lapko VA, Kiryushina EV, Vokin VN. Nonparametric pattern recognition algorithm for testing a hypothesis of the independence of random variables. Computer Optics 2021; 45(5): 767-772. DOI: 10.18287/2412-6179-CO-871.

Acknowledgements:
The research was funded by the Russian Foundation for Basic Research, government of Krasnoyarsk Territory, and Krasnoyarsk Regional Science Foundation under project No. 20-41-240001.

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