Article 1118

Title of the article

EVALUATION OF DATA INFORMATIVITY OF NORMAL HISTOGRAM AND SPECTRAL LINE OF OUTPUT STATES CHI-SQUARE MOLECULES FOR SMALL SELECTIONS 

Authors

Volchikhin Vladimir Ivanovich, Doctor of engineering sciences, professor, the President of Penza State University (40 Krasnaya street, Penza, Russia), president@pnzgu.ru
Ivanov Aleksandr Ivanovich, Doctor of engineering sciences, associate professor, head of the laboratory of biometric and neural network technologies, Penza Research Institute of Electrical Engineering (9 Sovetskaya street, Penza, Russia), ivan@pniei.penza.ru
Gazin Aleksey Ivanovich, Candidate of engineering sciences, associate professor, sub-department of informatics, information technologies and information protection, Lipetsk State Pedagogical P. Semenov-Tyan-Shansky University (42 Lenina street, Lipetsk, Russia), alexey_82@mail.ru
Serikova Yuliya Igorevna, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), julia-ska@yandex.ru

Index UDK

519.24; 53; 57.017

DOI

10.21685/2072-3059-2018-1-1

Abstract

Background. The research goal is to evaluate the informativeness of biometric data represented by usual histograms and strongly thinned histograms, which are the spectral lines at the chi-square output of a mathematical molecule.
Materials and methods. When synthesizing histograms from 7 columns on a samplein 21 an example of a biometric image a special condition is used. The mathematical expectation of the sample is accurately placed in the center of the central
column of the histogram. In this case, the output spectrum. The chi-square of the molecule becomes discrete and has 415 spectral lines of significant amplitude. In the article, it is suggested to evaluate the mutual informationality of the columns of histograms
and spectral lines for the normal and even-dimensional laws of distribution of values.
Results. It turned out that the informativeness of 7 columns of the usual histogram is always less than 10.71 bits. With the same rule for computing the informativeness of 218 spectral lines, the chi-square of the molecule is 536.5 bits. There is more than a 50-fold increase in the information content of these small samples, if we abandon the traditional application of the chi-square criterion.
Conclusions. The potential of analysis of the output discrete spectrum of the chisquare molecule is much higher than the potential of the usual statistical processing of the chi-square test data. In place of the 7 columns of the histogram, a heavily decimated
histogram with 415 columns is obtained, while the average informativity of the columns of the usual histogram is 1.53 bits, and the average information of the spectral lines (strongly thinned histogram) is -1.29 bits. Informative data processing parameters are comparable.

Key words

discrete spectrum of molecule hi-square state, statistical analysis of small samples, connection of continuous and discrete densities of chi-square distribution criterion

Download PDF
References

1. GOST R 52633.5–2011. Zashchita informatsii. Tekhnika zashchity informatsii. Avtomaticheskoe obuchenie neyrosetevykh preobrazovateley biometriya-kod dostupa [State Standard GOST R 52633.5-2011. Information protection. Information protection technique. Automatic learning of neural network "biometrics-access code" converters]. Moscow, 2011.
2. Kobzar' A. I. Prikladnaya matematicheskaya statistika. Dlya inzhenerov i nauchnykh rabotnikov [Applied mathematical statistics. For engineers and researchers]. Moscow: Fizmatlit, 2006, 816 p.
3. R 50.1.037–2002. Rekomendatsii po standartizatsii. Prikladnaya statistika. Pravila proverki soglasiya opytnogo raspredeleniya s teoreticheskim. Ch. I. Kriterii tipa χ2. Gosstandart Rossii [Recommendations for standardization. Applied statistics. Rules for
verifying the agreement of the experimental distribution with the theoretical distribution. Part I. Criteria of the type χ2. State standard of Russia]. Moscow, 2001, 140 p.
4. Akhmetov B. B., Ivanov A. I., Serikova N. I., Funtikova Yu. V. Vestnik Natsional'noy akademii nauk Respubliki Kazakhstan [Bulletin of the National Academy of Sciences of the Republic of Kazakhstan]. Almaty, 2015, no. 1, pp. 17–25.
5. Akhmetov B., Ivanov A., Gilmutdinov A., Bezyaev A., Funtikova Y. International Conference on New Directions in Multidisciplinary Research & Practice (NDMRP-15-265). Global Illuminators (April 22, 2015). Istanbul, Turkey, 2015.
6. Kulagin V. P., Ivanov A. I., Gazin A. I., Akhmetov B. B. Analitika [Analytics]. 2016, no. 5 (30), pp. 22–29.
7. Volchikhin V. I., Ivanov A. I., Pashchenko D. V., Akhmetov B. B., Vyatchanin S. E. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki [University proceedings. Volga region. Engineering sciences]. 2017, no. 1 (41), pp. 5–15.
8. Ivanov A. I. Mnogomernaya neyrosetevaya obrabotka biometricheskikh dannykh s programmnym vosproizvedeniem effektov kvantovoy superpozitsii [Multidimensional neural network processing of biometric data with software reproduction of quantum superposition effects]. Penza: AO «PNIEI», 2016, 133 p. Available at: http://pniei.pf/activity/science/BOOK16.pdf
9. Volchikhin V. I., Ivanov A. I., Gazin A. I., Bannih A. G. Journal of Computational and Engineering Mathematics. 2017, vol. 4, no. 4, pp. 53–63.
10. El'yashev M. A. Atomnaya i molekulyarnaya spektroskopiya. Obshchie voprosy spektroskopii [Atomic and molecular spectroscopy. General questions of spectroscopy]. Moscow: Izdatel'stvo URSS, 2014, 246 p.
11. El'yashev M. A. Atomnaya i molekulyarnaya spektroskopiya. Molekulyatnaya spektroskopiya [Atomic and molecular spectroscopy. Molecular spectroscopy]. Moscow: Izd-vo URSS, 2015, 528 p.
12. El'yashev M. A. Atomnaya i molekulyarnaya spektroskopiya. Atomnaya spektroskopiya [Atomic and molecular spectroscopy. Atomic spectroscopy]. Moscow: Izd-vo URSS, 2018, 416 p.
13. Ivanov A. I., Akhmetov B. B., Serikova Yu. I. Nadezhnost' i kachestvo slozhnykh system [Safety and quality of complex systems]. 2016, no. 4 (16), pp. 121–127.
14. Volchikhin V. I., Ivanov A. I., Serikov A. V., Serikova Yu. I. Vestnik Mordovskogo universiteta [Bulletin of Mordovia State University]. 2017, vol. 27, no. 2, pp. 230–243.
15. Volchikhin V. I., Ivanov A. I. Vestnik Mordovskogo universiteta [Bulletin of Mordovia State University]. 2017, vol. 27, no. 4, pp. 518–523.

 

Дата создания: 13.06.2018 14:02
Дата обновления: 03.07.2018 16:14