Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

Advertisement

Springer Nature Link
Log in

Machine learning-based classification of time series of chaotic systems

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

In this study, the classification of time series belonging to three different chaotic systems has been proposed using machine learning methods. For this purpose, the time series of Lorenz, Chen, and Rossler systems, three of the well-known chaotic systems, are classified using machine learning methods. In the study, the classification of chaotic systems has been made with 18 sub-methods of Naive Bayes, Support Vector Machines, K-Nearest Neighborhood, and Tree methods. As a result, the K-Nearest Neighborhood method has classified time series belonging to chaotic systems with very high accuracy of 99.2%. In this way, it has become possible to associate the chaotic-random signals with a mathematical system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. O. Sevli, Performance Comparison of Different Machine Learning Techniquesin Diagnosis of Breast Cancer. Eur. J. Sci. Technol. 16, 176–185 (2019)

    Article  Google Scholar 

  2. J. A. Cruz and D. S. Wishart, “Applications of machine learning in cancer prediction and prognosis,” Cancer Informatics, vol. 2. Libertas Academica Ltd., pp. 59–77, 2006

  3. Nonlinear forecasting for the classification of natural time series, Philos. Trans. R. Soc. London. Ser. A Phys. Eng. Sci., vol. 348, no. 1688, pp. 477–495, Sep. 1994

  4. M. Casdagli, Nonlinear prediction of chaotic time series. Phys. D Nonlinear Phenom. 35(3), 335–356 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  5. Y. C. Lai and N. Ye, Recent developments in chaotic time series analysis, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 6. World Scientific Publishing Co. Pte Ltd, pp. 1383–1422, 2003

  6. S. Mukherjee, E. Osuna, and F. Girosi, Nonlinear prediction of chaotic time series using support vector machines, in Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop, 1997, pp. 511–520

  7. K. He, X. Zhang, S. Ren, and J. Sun, Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification, in 2015 IEEE International Conference on Computer Vision (ICCV), 2015, vol. 2015 Inter, pp. 1026–1034

  8. J.B. Elsner, A.A. Tsonis, Nonlinear Prediction, Chaos, and Noise. Bull. Am. Meteorol. Soc. 73(1), 49–60 (1992)

    Article  ADS  Google Scholar 

  9. T. Kuremoto, S. Kimura, K. Kobayashi, M. Obayashi, Time series forecasting using a deep belief network with restricted Boltzmann machines. Neurocomputing 137, 47–56 (2014)

    Article  Google Scholar 

  10. Z. Wang, W. Yan, and T. Oates, Time series classification from scratch with deep neural networks: A strong baseline, in 2017 International Joint Conference on Neural Networks (IJCNN), 2017, vol. 2017-May, pp. 1578–1585

  11. J. Pathak, B. Hunt, M. Girvan, Z. Lu, and E. Ott, Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach, Phys. Rev. Lett., vol. 120, no. 2, Jan. 2018

  12. J. Pathak, Z. Lu, B. R. Hunt, M. Girvan, and E. Ott, Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data, Chaos, vol. 27, no. 12, Dec. 2017

  13. N. Boullé, V. Dallas, Y. Nakatsukasa, D. Samaddar, Classification of chaotic time series with deep learning. Phys. D Nonlinear Phenom. 403, 132261 (2020)

    Article  MathSciNet  Google Scholar 

  14. L. Zhang, EEG Signals Classification Using Machine Learning for the Identification and Diagnosis of Schizophrenia, in Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, 2019, pp. 4521–4524

  15. E. Sayilgan, Y. Kemal, Y.Y. Isler, Classification of Hand Movements from EEG Signals using Machine Learning Techniques, in Proceedings -, Innovations in Intelligent Systems and Applications Conference. ASYU 2019, 2019 (2019)

  16. P. Shimpi, S. Shah, M. Shroff, and A. Godbole, A machine learning approach for the classification of cardiac arrhythmia, in Proceedings of the International Conference on Computing Methodologies and Communication, ICCMC 2017, 2018, vol. 2018-January, pp. 603–607

  17. E. N. Lorenz, Deterministic nonperiodic flow, in Universality in Chaos, Second Edition, 2017, pp. 367–378

  18. M. Gorman, P.J. Widmann, K.A. Robbins, Nonlinear dynamics of a convection loop: A quantitative comparison of experiment with theory. Phys. D Nonlinear Phenom. 19(2), 255–267 (1986)

    Article  ADS  Google Scholar 

  19. H. Haken, Analogy between higher instabilities in fluids and lasers. Phys. Lett. A 53(1), 77–78 (1975)

    Article  ADS  Google Scholar 

  20. K.M. Cuomo, A.V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett. 71(1), 65–68 (1993)

    Article  ADS  Google Scholar 

  21. N. Hemati, Strange Attractors in Brushless DC Motors, IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 41(1), 40–45 (1994)

    Article  Google Scholar 

  22. E. Knobloch, Chaos in the segmented disc dynamo. Phys. Lett. A 82(9), 439–440 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  23. G. Chen, T. Ueta, Yet another chaotic attractor. Int. J. Bifurc. Chaos 9(7), 1465–1466 (1999)

    Article  MathSciNet  Google Scholar 

  24. O.E. Rössler, An equation for continuous chaos. Phys. Lett. A 57(5), 397–398 (1976)

    Article  ADS  Google Scholar 

  25. C. Cortes, V. Vapnik, Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)

    MATH  Google Scholar 

  26. L. Shen et al., Evolving support vector machines using fruit fly optimization for medical data classification. Knowl.-Based Syst. 96, 61–75 (2016)

    Article  Google Scholar 

  27. A. Wood, V. Shpilrain, K. Najarian, and D. Kahrobaei, Private naive bayes classification of personal biomedical data: Application in cancer data analysis, Artic. Comput. Biol. Med., 2018

  28. A. Tekerek, Support vector machine based spam SMS detection. J. Polytech. 22(2), 779–784 (2018)

    Google Scholar 

  29. W.A. Awad, S.M. Elseuofi, Machine Learning methods for E-mail Classification. Int. J. Comput. Appl. 16(1), 39–45 (2011)

    Google Scholar 

  30. S. Theodoridis, K. Koutroumbas, Pattern Recognition and Neural Networks, in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2049 (Springer Verlag, LNAI, 2001), pp. 169–195

  31. M.Ç. Aksu, E. Karaman, Karar Ağaçlarıile Bir Web Sitesinde Link Analizi ve Tespiti. Acta Infologica 1(2), 84–91 (2017)

    Google Scholar 

  32. G. Silahtaroğlu, Veri madenciliği (Papatya Yayıncılık Eğitim A.Ş, İstanbul, 2013)

    Google Scholar 

  33. G. Pehlivan, CHAID Analizi ve Bir Uygulama (Yıldız Teknik Üniversitesi, Fen Bilimleri Enstitüsü, FBE İstatistik Anabilimdalı, Yüksek Lisans Tezi, 2006)

  34. Ş Demirel, S.G. Yakut, Decision Tree Algorithms and an Application on Child Labor. Sos. Bilim. Araştırma Derg. 8(4), 52–65 (2019)

    Google Scholar 

  35. S. Özekes, Veri Madenciliği Modelleri ve Uygulama Alanları. İstanbul Ticaret Üniversitesi Derg. 3, 65–82 (2003)

    Google Scholar 

  36. M. Felkin, Comparing classification results between N-ary and binary problems. Stud. Comput. Intell. 43, 277–301 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Engineering, Faculty of Technology, Sakarya University of Applied Sciences, 54050, Sakarya, Turkey

    Süleyman Uzun

Authors
  1. Süleyman Uzun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Süleyman Uzun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Uzun, S. Machine learning-based classification of time series of chaotic systems. Eur. Phys. J. Spec. Top. 231, 493–503 (2022). https://doi.org/10.1140/epjs/s11734-021-00346-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-021-00346-z

Search

Navigation