Properties of the nonparametric decision function with a priori information on independence of attributes of classified objects

Лапко, А. В.; Лапко, В. А.

doi:10.3103/s8756699012040139

Cited by 9 publications

(3 citation statements)

References 2 publications

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“…«Красноярский рабочий», д. 31; 4 Федеральный исследовательский центр информационных и вычислительных технологий, 660049, г. Красноярск, просп. Мира, д.…”

Section: методика последовательного формирования набора компонент мно...unclassified

“…Априорная информация о независимости случайных величин позволяет повысить аппроксимационные свойства непараметрической оценки плотности вероятности типа Розенблатта-Парзена по сравнению с ядерной статистикой для зависимых переменных [1 -3]. Данный вывод подтверждается при анализе асимптотических свойств непараметрических решающих функций ядерного типа в задаче распознавания образов [4].…”

Section: Introductionunclassified

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A method of sequentially generating a set of components of a multidimensional random variable using a nonparametric pattern recognition algorithm

Zenkov

Лапко

et al. 2021

Computer Optics

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We study in which way a priori information on the independence of random variables affects the approximation accuracy of a nonparametric estimate of the Rosenblatt–Parzen probability density. A new technique for generating sets of independent components of a multidimensional random variable is proposed. The methodology is based on testing the hypotheses of the independence of combinations of the multidimensional random variable components using a two-alternative nonparametric kernel algorithm for pattern recognition corresponding to the maximum likelihood criterion. Classes correspond to the domains of definition of the probability densities of sets of independent and dependent components of the multidimensional random variable. Nonparametric statistics of the kernel type are used to estimate the probability densities. The choice of the bandwidths of the kernel estimates of the probability densities is made from the condition of the minimum root-mean-square criterion. The sequential procedure for generating a set of independent components begins with the analysis of paired combinations of components of a multidimensional random variable. For each pair of components, the probability of an error in recognizing classes corresponding to the assumptions of independence and dependence of the considered components is estimated. A pair of components with the maximum difference between these errors is determined. If the errors obtained do not differ significantly, then there are no independent components in the considered multivariate random variable. If there is a significant difference in the probability estimates of class recognition errors, a pair of independent components is established. These components are included in a three-component set of a multidimensional random variable. The analysis of their combinations is carried out in the same way, following the above-described procedure. The process of generating the set of independent components is stopped when no reliable difference occurs any more between the probabilities of errors in recognizing situations belonging to the accepted classes. In this case, the previous set of independent components is the desired result. In contrast to the traditional methodology based on the Pearson criterion, the proposed approach allows us to bypass a problem of the decomposition of the range of values of random variables into multidimensional intervals. The method of generating a set of independent components of a multidimensional random variable is illustrated by the results of the analysis of spectral features of remote sensing data of forest tracts using space imagery from the Landsat-8 satellite.

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Section: методика последовательного формирования набора компонент мно...unclassified

Section: Introductionunclassified

A method of sequentially generating a set of components of a multidimensional random variable using a nonparametric pattern recognition algorithm

Zenkov

Лапко

et al. 2021

Computer Optics

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“…At the proof of the theorem the technique offered in work [3] and developed in [4][5][6][7][8] is used.…”

Section: Properties Of Nonparametric Estimates Of the Probabilitymentioning

confidence: 99%

Testing of hypothesis o f random variables independence on the basis of nonparametric algorithm of pattern recognition

Лапко

Yuronen

Лапко

2016

2016 International Siberian Conference on Control and Communications (SIBCON)

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Images identification by convolution methods under conditions of small observation samples

Petrovna,

Mamatkulova,

Nabiev

et al. 2023

AIP Conference Proceedings

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Properties of the nonparametric decision function with a priori information on independence of attributes of classified objects

Cited by 9 publications

References 2 publications

A method of sequentially generating a set of components of a multidimensional random variable using a nonparametric pattern recognition algorithm

A method of sequentially generating a set of components of a multidimensional random variable using a nonparametric pattern recognition algorithm

Testing of hypothesis o f random variables independence on the basis of nonparametric algorithm of pattern recognition

Images identification by convolution methods under conditions of small observation samples

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