Geodesic
Statistical method of recognizing on the base of nonlinear regression
Matematičeskoe modelirovanie, Tome 32 (2020) no. 4, pp. 116-130.

Voir la notice de l'article provenant de la source Math-Net.Ru

The work is devoted to the statistical method of classification based on nonlinear regression. The ways of its implementation in solving the problem of recognition of printed and handwritten characters, as well as for the first time for assessing the health of the systems of the human body according to the parameters of peripheral blood. The optimal structure of polynomials is proposed. The properties of the probability estimates generated by the method are described. The structure of the sets used for its training is analyzed.
Keywords: recognition, statistical method, printed symbol, handwritten symbol, human health condition, body system, peripheral blood.
Mots-clés : classification, polynomial regression 
@article{MM_2020_32_4_a8,
     author = {B. M. Gavrikov and M. B. Gavrikov and N. V. Pestryakova},
     title = {Statistical method of recognizing on the base of nonlinear regression},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {116--130},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_4_a8/}
}
TY  - JOUR
AU  - B. M. Gavrikov
AU  - M. B. Gavrikov
AU  - N. V. Pestryakova
TI  - Statistical method of recognizing on the base of nonlinear regression
JO  - Matematičeskoe modelirovanie
PY  - 2020
SP  - 116
EP  - 130
VL  - 32
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2020_32_4_a8/
LA  - ru
ID  - MM_2020_32_4_a8
ER  - 
%0 Journal Article
%A B. M. Gavrikov
%A M. B. Gavrikov
%A N. V. Pestryakova
%T Statistical method of recognizing on the base of nonlinear regression
%J Matematičeskoe modelirovanie
%D 2020
%P 116-130
%V 32
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2020_32_4_a8/
%G ru
%F MM_2020_32_4_a8
B. M. Gavrikov; M. B. Gavrikov; N. V. Pestryakova. Statistical method of recognizing on the base of nonlinear regression. Matematičeskoe modelirovanie, Tome 32 (2020) no. 4, pp. 116-130. http://geodesic.mathdoc.fr/item/MM_2020_32_4_a8/

[1] M. B. Gavrikov, N. V. Pestriakova, “Metod polinomialnoi regressii v zadachakh raspoznavaniia pechatnykh i rukopechatnykh simvolov”, Keldysh Institute preprints, 2004, 022, 12 pp.

[2] M. B. Gavrikov, A. V. Misyurev, N. V. Pestriakova, O. A. Slavin, “On a Pattern Recognition Method Based on Polynomial Regression”, Automation and Remote Control, 67:2 (2006), 278–292 | DOI | MR | Zbl

[3] N. V. Pestriakova, Metod raspoznavaniia simvolov, osnovannyi na polinomialnoi regressii, URSS, M., 2011, 141 pp.

[4] M. B. Gavrikov, N. V. Pestriakova, B. M. Gavrikov, “Ob effektivnykh prilozheniiakh polinomialnoi regressii k zadache raspoznavaniia simvolov”, Trudy ISA RAN, 64:4 (2014), 89–96

[5] B. M. Gavrikov, M. B. Gavrikov, N. V. Pestriakova, “Statisticheskii analiz kharakteristik metoda raspoznavaniia na obuchayushchem mnozhestve”, Informatsionnye tekhnologii i vychislitelnye sistemy, 2015, no. 2, 50–67 | MR

[6] B. M. Gavrikov, M. B. Gavrikov, I. M. Lebedenko, N. V. Pestriakova, R. V. Stavitskii, “Metod otsenivaniia sostoyaniia zdorovia cheloveka”, Keldysh Institute preprints, 2017, 008, 18 pp.

[7] B. M. Gavrikov, M. B. Gavrikov, N. V. Pestriakova, R. V. Stavitskii, “Struktura bazy obucheniia statisticheskogo klassifikatora sostoianii sistem organizma cheloveka”, Keldysh Institute preprints, 2018, 255, 40 pp.

[8] V. V. Arlazarov, A. E. Zhukovskii, V. E. Krivtsov, D. P. Nikolaev, D. V. Poleviy, “Analiz osobennostei ispolzovaniia statsionarnykh i mobilnykh malorazmernykh tsifrovykh video kamer dlia raspoznavaniia dokumentov”, Inform. tekhn. i vych. sist., 2014, no. 3, 71–81

[9] O. O. Petrova, K. B. Bulatov, “Metody post-obrabotki rezultatov raspoznavaniia mashinochitaemoi zony dokumentov”, Trudy Instituta sistemnogo analiza RAN, 2018, Spetsialnyi vypusk, 43–50

[10] V. V. Arlazarov, K. B. Bulatov, A. V. Uskov, “Model sistemy raspoznavaniia oiektov v videopotoke mobilnogo ustroistva”, Trudy Instituta sistemnogo analiza RAN, 2018, Spetsialnyi vypusk, 73–82

[11] R. V. Stavitskii, L. A. Lebedev, A. L. Lebedev, A. Iu. Smyslov, Kolichestvennaia otsenka go-meostaticheskoi aktivnosti zdorovykh i bolnykh liudei, GART, M., 2013, 131 pp.

[12] N. Iu. Dobrovolskaia, L. A. Lebedev, A. L. Lebedev, Iu. B. Novozhilov, R. V. Stavitskii, “Khimio-luchevaia terapiia raka sheiki matki. Metodika otsenki sostoianiia organizma i ego sistem”, Radiologiia-praktika, 2011, no. 3, 53–63

[13] I. M. Lebedenko, T. Z. Cherniavskaya, R. V. Stavitskii, O. N. Plautin, “Tekhnicheskii control sostoyaniia organizma i ego sistem v protsesse khimio-luchevoi terapii i transplantatsii kostnogo mozga pri ostrykh leikozakh”, Meditsinskaia tekhnika, 2014, no. 5, 32–36

[14] Iu. A. Tsybulskaia, R. V. Stavitskii, I. M. Lebedenko, S. V. Smerdin, I. V. Shutikhina, L. S. Kokov, O. V. Baturin, “Kolichestvennyi podkhod k diagnostike porazheniia kostno-sustavnoy sistemy pri tuberkuleznom spondilite”, Meditsinskii vestnik Severnogo Kavkaza, 2015, no. 3, 212–217

[15] A. B. Merkov, Raspoznavaniie obrazov. Vvedeniie v metody statisticheskogo obucheniia, izd. 2, ispr., URSS, M., 2019, 256 pp.

[16] A. B. Merkov, Raspoznavaniie obrazov. Postroyeniie i obuchenie veroyatnostnykh modelei, URSS., M., 2014, 240 pp.

[17] K. V. Vorontsov, Matematicheskiie metody obucheniia po pretsedentam, Kurs lektsii, MFTI, Dolgoprudnyi, 2012

[18] Iu. V. Linnik, Metod naimenshikh kvadratov i osnovy matematiko-statisticheskoi teorii obrabotki nabliudenii, Fizmatlit, M., 1958, 336 pp.

[19] M. B. Gavrikov, O. V. Lokutsievskii, Nachala chislennogo analiza, Ianus, M., 1995, 581 pp. | MR

[20] J. Schürmann, Pattern Classification, John Wiley, Inc., New York, 1996, 374 pp. | MR