DOI: https://doi.org/10.15587/1729-4061.2014.21869

Adaptive polynomial neuronetwork predicting model of time series and its training

Елена Вадимовна Мантула, Сергей Владимирович Машталир

Abstract


The relevance to develop new predicting methods is caused by their vital importance in solving various tasks of industrial, agricultural, financial-economic, medico-biologic and ecological systems.

The problem of predicting non-stationary non-linear time series under limited amount of a priori information is considered in the paper. To solve it, the method for synthesizing polynomial neural networks, which is an alternative to multilayer perceptrons and radial-basis neural networks, the use of which has several drawbacks, limiting their use in solving many practical problems is proposed. The advantage of the proposed predicting method over traditional neural networks is the ease of numerical implementation, essential reduction in time to perform the operation, this method allows to handle significantly non-stationary processes, containing both irregular trends, and sudden jumps, and allows to complicate the architecture of neural networks without the need to recalculate already adjusted synaptic weights. Training by epochs, used in training multilayer networks can be used for training such neural network. That is why, since only one hidden layer is studied, the considered neuronetwork model is still configured faster than the standard three-layer perceptron.


Keywords


predicting model; polynomial orthogonal neural network; Chebyshev polynomials; ortho-synapse; synaptic weights

References


Хайкин, С. Нейронные сети: полный курс [Текст] / C. Хайкин. – М.: Изд. дом «Вильямс», 2006. – 1104 с.

Pao, Y. H. Adaptive Pattern Recognition and Neural Networks [Text] / Y. H. Pao. – Reading, MA: Addison-Wesley, 1989 – 320 p.

Yang, S.-S. An ortonormal neural network for function approximation [Text] / S.-S. Yang, C.-S. Tseng // IEEE Transactions on Systems, Man, and Cybernetics. – 1996. – Vol. 26, № 12. – P. 925–935.

Lee, T. T. The Chebyshev polynomial-based unified model neural networks for function approximation [Text] / T. T. Lee, J. T. Jeng // IEEE Transactions on Systems, Man, and Cybernetics. – 1998. – Vol. 28, № 12. – P. 925–935.

Patra, J. C. Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks [Text] / J. C. Patra, A. C. Kot // IEEE Transactions on Systems, Man, and Cybernetics. – 2002. – Vol. 32, №4. – P. 505–511.

Бодянский, Е. В. Искусственные нейронные сети: архитектуры, обучение, применение [Текст] / Е. В. Бодянский, О. Г. Руденко // Харьков. ТЕЛЕТЕХ, 2004. – 372 с.

Бидюк, П. И. Методы прогнозирования [Текст] : Т. 1/ П. И. Бидюк, О. С. Меняйленко, О. С. Половцев. – Луганск: Альма-матер, 2008 – 301 с.

Бидюк, П. И. Методы прогнозирования [Текст] : Т. 2 / П. И. Бидюк, О. С. Меняйленко, О. С. Половцев. – Луганск: Альма-матер, 2008 – 305 с.

Райбман, Н. С. Построение моделей процессов производства [Текст] / Н. С. Райбман, В. М. Чадеев. – М.: Энергия, 1975. – 376 с.

Бодянский, Е. В. Ортосинапс, ортонейроны и нейропредиктор на их основе [Текст] / Е. В. Бодянский, Е. А. Викторов, А. Н. Слипченко // Системи обробки iнформації. – 2007. – Вип. 4 (62). – С. 139–143.

Бодянский, Е. В. Субоптимальное управление стохастическими процессами [Текст] / Е. В. Бодянский, С. Г. Удовенко, А. Е. Ачкасов, Г. К. Вороновский. – Харьков: Основа, 1997. – 140 с.

Перельман, И. И. Оперативная идентификация объектов управления [Текст] / И. И. Перельман. – М: Энергоатомиздат, 1982. – 272 с.

Haykin, S. (2006). Neural networks: a complete course. Moscow: Williams, 1104.

Pao, Y. H. (1989). Adaptive Pattern Recognition and Neural Networks. MA: Addison-Wesley, 320.

Yang, S.-S, Tseng, S.-S. (1996). An ortonormal neural network for function approximation. IEEE Transactions on Systems, Man and Cybernetics, 26 (12), 925–935.

Lee, T. T., Jeng, J. T. (1998). The Chebyshev polynomial-based unified model neural networks for function approximation. IEEE Transactions on Systems, Man, and Cybernetics, 28 (12), 925–935.

Patra, J. C., Kot, A. C. (2002). Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Transactions on Systems, Man, and Cybernetics, 32 (4), 505–511.

Bodyanskiy, E. V., Rudenko O. G. Artificial neural networks: architecture, training, application. (2004). Kharkiv: TELETEH, 372.

Bidyuk, P. I., Menyailenko O. S, Polovtsiev O. S. Prediction methods. (2008). Lugansk: Alma Mater, 301.

Bidyuk, P. I., Menyailenko, O. S, Polovtsiev, O. S. Prediction methods (2008). Lugansk: Alma Mater, 305.

Rajbman, N. S., V. M. Chadeev (1975). Postroenie modelej processov proizvodstva. Jenergija, 376.

Bodyanskiy, E. V., Victorov, E. A., Slipchenko, A. N. (2007). Ortosinaps, ortoneural and based on them neural prediktor. Information processing systems, 4 (62), 139–143.

Bodyanskiy, E. V., Udovenko S. G., Achkasov A. E., Voronovskiy G. K. (1997) Suboptimal control of stochastic processes. Kharkiv: Osnova, 140.

Perel’man, I. I. (1982). Operativnaja identifikacija obektov upravlenija. Jenergoatomizdat, 272.


GOST Style Citations








Copyright (c) 2014 Елена Вадимовна Мантула, Сергей Владимирович Машталир

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN (print) 1729-3774, ISSN (on-line) 1729-4061