PRECISION STATISTICS: NEUROET NETWORKING OF CHI-SQUARE TEST AND SHAPIRO–WILK TEST
IN THE ANALYSIS OF SMALL SELECTIONS OF BIOMETRIC DATA 

Иванов Александр Иванович, доктор технических наук, доцент, ведущий научный сотрудник, Пензенский научно-исследовательский электротехнический институт (440000, Россия, Пенза, Советская площадь, 9), E-mail: bio.ivan.penza@mail.ru
Вятчанин Сергей Евгеньевич, доцент, начальник кафедры радио- и космической связи, Пензенский государственный университет (440026, Россия, г. Пенза, ул. Красная, 40), E-mail: ivo@.pnzgu.ru
Малыгина Елена Александровна, кандидат технических наук, научный сотрудник, межотраслевая лаборатория тестирования биометрических устройств и технологий, Пензенский государственный университет (440026, Россия, г. Пенза, ул. Красная, 40), E-mail: e-mail: ivo@.pnzgu.ru
Лукин Виталий Сергеевич, аспирант, Пензенский государственный университет (440026, Россия, г. Пенза, ул. Красная, 40), E-mail: ivo@.pnzgu.ru 

519: 24; 53; 57.017 

DOI

10.21685/2307-4205-2019-2-4 

The aim of the paper is a neural network generalization of the Chi-square test and the Shapiro–Wilk test for the analysis of small samples of biometric data. It is shown that any of the statistical criteria can be represented in the form corresponding to a neuron having an input sorter, an adder and some functional converter. The generalization of two statistical criteria is accomplished by tuning the output quantizers of two neurons. The setting is always ambiguous for a predetermined value of the confidence probabilities of the generalized decisions. It is shown that the usual form of presentation of statistical criteria in the form of computational formulas and the tables of quantiles of confidence probability of the equivalent to their neural network description if the tables of the ratio of quantization thresholds providing a given level of confidence in a neural network generalization are given. 

Ключевые слова

the Chi-square test; the Shapiro–Wilk test; the neural network generalization of statistical criteria 

 Скачать статью в формате PDF

1. GOST R 52633.5-2011 Information protection. Information protection technology. Automatic learning of neural network converters biometry-access code.
2. Technical specification (project, public discussion started on 01.02.2017 by members of TK 26 "Cryptographic protection of information") PROTECTION OF NEUROET-NET BIOMETRIC CONTAINERS WITH THE USE OF CRYPTOGRAPHIC ALGORITHMS.
3. Р 50.1.037-2002 Recommendations of standardization. Applied statistics. Rules for verifying the agreement between the experimental distribution and the theoretical distribution. Part I. Criteria of the type χ2. State standard of Russia. – Moscow, 2001. – 140 p.
4. Kobzar, A. I. Applied mathematical statistics. For engineers and scientists / A. I. Kobzar. – Moscow : FIZMATLIT, 2006. – 816 p.
5. GOST R 52633.3-2011 Information protection. Information protection technology. Testing the robustness of highly reliable biometric protection to assault attacks.
6. Akhmetov, B. S. Algorithms for testing of biometric-neural network mechanisms of information protection / B. S. Akhmetov, V. I. Volchikhin, A. I. Ivanov, A.Y. Malygin. – Kazakhstan, Almaty, KazNTU Satpayev, 2013. – 152 p. – URL: http://portal.kazntu.kz/files/publicate/2014-01-04-11940.pdf
7. Akhmetov, B. B. Multidimensional statistics of essentially dependent biometric data, which are generated by neural network emulators of quadratic forms : monograph / B. B. Akhmetov, A. I. Ivanov. – Kazakhstan, Almaty : From LEM, 2016. – 86 p.
8. Volchikhin, V. I. Absolutely stable algorithm of automatic learning of networks of probabilistic neurons "Kramervon Mises" on small samples of biometric data / V. I. Volchikhin, A. I. Ivanov, S. E. Vjatchanin, E. A. Malygina // Izvestiya Vysshikh Uchebnykh Zavedenii. The Volga region. Technical science. – 2017. – № 2 (42). – P. 55–65.
9. Justification and selection of statistical criteria for correct evaluation of small samples data of biometric images / A. I. Ivanov, E. A. Malygina, Yu. I. Serikova, S. E. Vjatchanin, E. N. Kupriyanov // Proceedings of the International Symposium Reliability and quality. – 2018. – Vol. 1. – P. 176–178.
10. Neural networks improve the quality of decisions by switching from a double quantization functions to functions of quantization with multiple levels / E. A. Malygina, A. I. Solopov, Yu. I. Serikova, A. I. Gazin,
E. N. Kupriyanov // Proceedings of the International Symposium Reliability and quality. – 2018. – Vol. 1. – P. 182–183.
11. Features testing neural network converters biometrics code on small test samples of alien images / V. I. Volchihin, A. Yu. Malygin, I. V. Urnev, A. V. Serikov, E. N. Kupriyanov // Proceedings of the International Symposium Reliability and quality. – 2018. – Vol. 1. – P. 52–53.