Geodesic
Multi-parametric classification of automaton Markov models based on the sequences they generate
Prikladnaâ diskretnaâ matematika, no. 4 (2010), pp. 41-54.

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

This article is devoted to multi-parametric classification of automaton Markov models (AMMs) on the base of output sequences with the use of discriminant analysis. The AMMs under consideration are specified by means of stochastic matrices belonging to subclasses defined a priori. A set of claasification features is introduced to distinguish AMMs specified by matrices from different subclasses. The features are related to the frequency characteristics of sequences generated by AMMs. A method is suggested for determining the minimal length of the sequence need to calculate the features with a required accuracy.
Mots-clés : Markov chain, identification
Keywords: ergodic stochastic matrix, automaton Markov model, discriminant analysis, linear discriminant functions. 
@article{PDM_2010_4_a4,
     author = {A. R. Nurutdinova and S. V. Shalagin},
     title = {Multi-parametric classification of automaton {Markov} models based on the sequences they generate},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {41--54},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2010_4_a4/}
}
TY  - JOUR
AU  - A. R. Nurutdinova
AU  - S. V. Shalagin
TI  - Multi-parametric classification of automaton Markov models based on the sequences they generate
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2010
SP  - 41
EP  - 54
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2010_4_a4/
LA  - ru
ID  - PDM_2010_4_a4
ER  - 
%0 Journal Article
%A A. R. Nurutdinova
%A S. V. Shalagin
%T Multi-parametric classification of automaton Markov models based on the sequences they generate
%J Prikladnaâ diskretnaâ matematika
%D 2010
%P 41-54
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2010_4_a4/
%G ru
%F PDM_2010_4_a4
A. R. Nurutdinova; S. V. Shalagin. Multi-parametric classification of automaton Markov models based on the sequences they generate. Prikladnaâ diskretnaâ matematika, no. 4 (2010), pp. 41-54. http://geodesic.mathdoc.fr/item/PDM_2010_4_a4/

[1] Kemeni Dzh.,Snell Dzh., Konechnye tsepi Markova, Nauka, M., 1970, 272 pp.

[2] Romanovskii V. I., Diskretnye tsepi Markova, Gostekhizdat, M.–L., 1949, 436 pp. | MR

[3] Raskin L. G., Analiz stokhasticheskikh sistem i elementy teorii optimalnogo upravleniya, Sov. radio, M., 1976, 344 pp. | MR | Zbl

[4] Bukharaev R. G., Osnovy teorii veroyatnostnykh avtomatov, Nauka, M., 1985, 287 pp. | MR | Zbl

[5] Pospelov D. A., Veroyatnostnye avtomaty, Energiya, M., 1970, 88 pp. | MR

[6] Alferov A. P., Zubov A. Yu., Kuzmin A. S., Cheremushkin A. V., Osnovy kriptografii, Gelios ARV, M., 2002, 480 pp.

[7] Friedman W. F., Callimahos D., Military crypto analyze, Part I, V. Z. Aegean Park Press, Laguna Hills, CA, 1985, 356 pp.

[8] Borovikov V. P., Statistica: iskusstvo analiza dannykh na kompyutere, 2-e izd., Piter, SPb., 2003, 700 pp.

[9] Zakharov V. M., Nurmeev N. N., Salimov F. I. i dr., “K zadache diskriminantnogo analiza avtomatnykh markovskikh modelei”, Vestnik KGTU im. A. N. Tupoleva, 1:3 (2001), 37–39

[10] Zakharov V. M., Nurmeev N. N., Salimov F. I., Shalagin S. V., “Klassifikatsiya stokhasticheskikh ergodicheskikh matrits metodami klasternogo i diskriminantnogo analiza”, Issledovaniya po informatike, 2, Otechestvo, Kazan, 2000, 91–106

[11] Li I., Dzhadzh D., Zelner A. M., Otsenivanie parametrov markovskoi modeli po agregirovannym vremennym ryadam, Statistika, M., 1977, 221 pp.

[12] Lankaster L., Teoriya matrits, Nauka, M., 1982, 272 pp. | MR

[13] Khinchin A. Ya., “Ponyatie entropii v teorii veroyatnostei”, Uspekhi matem. nauk, 8:3(55) (1953), 3–20 | MR | Zbl

[14] Sabitova A. R., Shalagin S. V., “Diskriminantnyi analiz veroyatnostnykh modelei markovskogo tipa”, Nauka. Tekhnologii. Innovatsii, Materialy Vseros. konf. molodykh uchenykh, Izd-vo NGTU, Novosibirsk, 2007, 90–92

[15] Sabitova A. R., Shalagin S. V., “Mnogoparametricheskaya klassifikatsiya markovskikh posledovatelnostei”, XV Tupolevskie chteniya, Mezhdunar. molodezhnaya nauch. konf., Izd-vo KGTU im. A. N. Tupoleva, Kazan, 2007, 78–79

[16] Nurutdinova A. R., Shalagin S. V., “Metodika identifikatsii avtomatnykh markovskikh modelei na osnove porozhdaemykh imi posledovatelnostei”, Vestnik KGTU im. A. N. Tupoleva, 2010, no. 1, 94–99

[17] Venttsel E. S., Teoriya veroyatnostei, IV izd., ster., Nauka, M., 1969, 576 pp. | MR | Zbl