Adaptive polynomial neuronetwork predicting model of time series and its training

Authors

DOI:

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

Keywords:

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

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.

Author Biographies

Елена Вадимовна Мантула, Kharkiv National University of Radio Electronics, Ukraine

Postgraduate Student at the Informatics Department

Сергей Владимирович Машталир, Kharkiv National University of Radio Electronics, Ukraine, Cand. Sc. (Technology)

Associate Professor at the Informatics Department

References

  1. Хайкин, С. Нейронные сети: полный курс [Текст] / C. Хайкин. – М.: Изд. дом «Вильямс», 2006. – 1104 с.
  2. Pao, Y. H. Adaptive Pattern Recognition and Neural Networks [Text] / Y. H. Pao. – Reading, MA: Addison-Wesley, 1989 – 320 p.
  3. 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.
  4. 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.
  5. 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.
  6. Бодянский, Е. В. Искусственные нейронные сети: архитектуры, обучение, применение [Текст] / Е. В. Бодянский, О. Г. Руденко // Харьков. ТЕЛЕТЕХ, 2004. – 372 с.
  7. Бидюк, П. И. Методы прогнозирования [Текст] : Т. 1/ П. И. Бидюк, О. С. Меняйленко, О. С. Половцев. – Луганск: Альма-матер, 2008 – 301 с.
  8. Бидюк, П. И. Методы прогнозирования [Текст] : Т. 2 / П. И. Бидюк, О. С. Меняйленко, О. С. Половцев. – Луганск: Альма-матер, 2008 – 305 с.
  9. Райбман, Н. С. Построение моделей процессов производства [Текст] / Н. С. Райбман, В. М. Чадеев. – М.: Энергия, 1975. – 376 с.
  10. 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.
  11. 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.
  12. Перельман, И. И. Оперативная идентификация объектов управления [Текст] / И. И. Перельман. – М: Энергоатомиздат, 1982. – 272 с.
  13. Haykin, S. (2006). Neural networks: a complete course. Moscow: Williams, 1104.
  14. Pao, Y. H. (1989). Adaptive Pattern Recognition and Neural Networks. MA: Addison-Wesley, 320.
  15. 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.
  16. 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.
  17. 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.
  18. Bodyanskiy, E. V., Rudenko O. G. Artificial neural networks: architecture, training, application. (2004). Kharkiv: TELETEH, 372.
  19. Bidyuk, P. I., Menyailenko O. S, Polovtsiev O. S. Prediction methods. (2008). Lugansk: Alma Mater, 301.
  20. Bidyuk, P. I., Menyailenko, O. S, Polovtsiev, O. S. Prediction methods (2008). Lugansk: Alma Mater, 305.
  21. Rajbman, N. S., V. M. Chadeev (1975). Postroenie modelej processov proizvodstva. Jenergija, 376.
  22. 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.
  23. Bodyanskiy, E. V., Udovenko S. G., Achkasov A. E., Voronovskiy G. K. (1997) Suboptimal control of stochastic processes. Kharkiv: Osnova, 140.
  24. Perel’man, I. I. (1982). Operativnaja identifikacija obektov upravlenija. Jenergoatomizdat, 272.

Downloads

Published

2014-04-09

How to Cite

Мантула, Е. В., & Машталир, С. В. (2014). Adaptive polynomial neuronetwork predicting model of time series and its training. Eastern-European Journal of Enterprise Technologies, 2(4(68), 16–20. https://doi.org/10.15587/1729-4061.2014.21869

Issue

Vol. 2 No. 4(68) (2014): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

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.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.