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

Deep learning based classification of time series of chaotic systems over graphic images

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this study, for the first time in the literature, identification of different chaotic systems by classifying graphic images of their time series with deep learning methods is aimed. For this purpose, a data set is generated that consists of the graphic images of time series of the most known three chaotic systems: Lorenz, Chen, and Rossler systems. The time series are obtained for different parameter values, initial conditions, step size and time lengths. After generating the data set, a high-accuracy classification is performed by using transfer learning method. In the study, the most accepted deep learning models of the transfer learning methods are employed. These models are SqueezeNet, VGG-19, AlexNet, ResNet50, ResNet101, DenseNet201, ShuffleNet and GoogLeNet. As a result of the study, classification accuracy is found between 96% and 97% depending on the problem. Thus, this study makes association of real time random signals with a mathematical system possible.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

No Data Availability.

References

  1. Agarwal A, Patni K, Rajeswari D (2021) Lung cancer detection and classification based on alexnet CNN. In: Proceedings of the 6th International Conference on Communication and Electronics Systems, ICCES 2021, Jul. 2021, pp 1390–1397. https://doi.org/10.1109/ICCES51350.2021.9489033

    Chapter  Google Scholar 

  2. Aksoy B, Halis HD, Salman OKM (2020) Identification of diseases in apple plants with artificial intelligence methods and comparison of the performance of artificial intelligence methods. Int J Eng Innov Res 2(3):194–210. https://doi.org/10.47933/ijeir.772514

    Article  Google Scholar 

  3. Altan G (2019) DeepGraphNet: Grafiklerin Sınıflandırılmasında Derin Öğrenme Modelleri. Eur J Sci Technol:319–327. https://doi.org/10.31590/ejosat.638256

  4. Arena P, Calí M, Patané L, Portera A, Spinosa AG (2019) A CNN-based neuromorphic model for classification and decision control. Nonlinear Dyn 95(3):1999–2017. https://doi.org/10.1007/s11071-018-4673-4

    Article  Google Scholar 

  5. Balagourouchetty L, Pragatheeswaran JK, Pottakkat B, Ramkumar G (2020) GoogLeNet-based ensemble FCNet classifier for focal liver lesion diagnosis. IEEE J Biomed Heal Informatics 24(6):1686–1694. https://doi.org/10.1109/JBHI.2019.2942774

    Article  Google Scholar 

  6. Ballester P, Araujo RM (2016) On the performance of googlenet and alexnet applied to sketches. In: 30th AAAI conference on artificial intelligence, AAAI 2016, pp 1124–1128

    Google Scholar 

  7. Barros P, Parisi GI, Weber C, Wermter S (2017) Emotion-modulated attention improves expression recognition: a deep learning model. Neurocomputing 253:104–114. https://doi.org/10.1016/j.neucom.2017.01.096

    Article  Google Scholar 

  8. Boullé N, Dallas V, Nakatsukasa Y, Samaddar D (2020) Classification of chaotic time series with deep learning. Phys D Nonlinear Phenom 403:132261. https://doi.org/10.1016/j.physd.2019.132261

    Article  MathSciNet  Google Scholar 

  9. Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9(7):1465–1466. https://doi.org/10.1142/S0218127499001024

    Article  MathSciNet  Google Scholar 

  10. Cuomo KM, Oppenheim AV (1993) Circuit implementation of synchronized chaos with applications to communications. Phys Rev Lett 71(1):65–68. https://doi.org/10.1103/PhysRevLett.71.65

    Article  Google Scholar 

  11. Dang W, Gao Z, Sun X, Li R, Cai Q, Grebogi C (2020) Multilayer brain network combined with deep convolutional neural network for detecting major depressive disorder. Nonlinear Dyn. 102(2):667–677. https://doi.org/10.1007/s11071-020-05665-9

    Article  Google Scholar 

  12. Deng L, Liu Y (2018) Deep learning in natural language processing. Springer Singapore, Singapore

    Book  Google Scholar 

  13. Dhungel N, Carneiro G, Bradley AP (2017) Combining deep learning and structured prediction for segmenting masses in mammograms. In: Advances in computer vision and pattern recognition, no. 9783319429984, pp 225–240

    Google Scholar 

  14. Duque AB, Santos LLJ, Macêdo D, Zanchettin C (2019) Squeezed very deep convolutional neural networks for text classification. In: Lecture notes in computer science, vol. 11727 LNCS, pp 193–207. https://doi.org/10.1007/978-3-030-30487-4_16

    Chapter  Google Scholar 

  15. Gaikwad AS, El-Sharkawy M (2018) Pruning convolution neural network (squeezenet) using taylor expansion-based criterion. In: 2018 IEEE international symposium on signal processing and information technology, ISSPIT 2018, Dec. 2018, vol. 2019-Janua, pp 1–5. https://doi.org/10.1109/ISSPIT.2018.8705095

    Chapter  Google Scholar 

  16. Gonzalez TF (2007) Handbook of approximation algorithms and metaheuristics. Chapman and Hall/CRC

    Book  Google Scholar 

  17. Gorman M, Widmann PJ, Robbins KA (1986) Nonlinear dynamics of a convection loop: a quantitative comparison of experiment with theory. Phys D Nonlinear Phenom 19(2):255–267. https://doi.org/10.1016/0167-2789(86)90022-9

    Article  Google Scholar 

  18. Guo Y, Liu Y, Oerlemans A, Lao S, Wu S, Lew MS (2016) Deep learning for visual understanding: a review. Neurocomputing 187:27–48. https://doi.org/10.1016/j.neucom.2015.09.116

    Article  Google Scholar 

  19. Haken H (1975) Analogy between higher instabilities in fluids and lasers. Phys Lett A 53(1):77–78. https://doi.org/10.1016/0375-9601(75)90353-9

    Article  Google Scholar 

  20. Han X, Zhong Y, Cao L, Zhang L (2017) Pre-trained alexnet architecture with pyramid pooling and supervision for high spatial resolution remote sensing image scene classification. Remote Sens 9(8):848. https://doi.org/10.3390/rs9080848

    Article  Google Scholar 

  21. Haskins G, Kruger U, Yan P (2020) Deep learning in medical image registration: a survey. Mach Vis Appl 31(1):8. https://doi.org/10.1007/s00138-020-01060-x

    Article  Google Scholar 

  22. He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: 2016 IEEE conference on computer vision and pattern recognition (CVPR), Jun. 2016, vol. 2016-Decem, pp 770–778. https://doi.org/10.1109/CVPR.2016.90

    Chapter  Google Scholar 

  23. Hemati N (1994) Strange attractors in brushless DC motors. IEEE Trans Circ Syst I Fundam Theory Appl 41(1):40–45. https://doi.org/10.1109/81.260218

    Article  Google Scholar 

  24. Huang G, Liu Z, Van Der Maaten L, Weinberger KQ (2017) Densely connected convolutional networks. In: 2017 IEEE conference on computer vision and pattern recognition (CVPR), Jul. 2017, vol. 2017-Janua, pp 2261–2269. https://doi.org/10.1109/CVPR.2017.243

    Chapter  Google Scholar 

  25. Iandola FN, Han S, Moskewicz MW, Ashraf K, Dally WJ, Keutzer K (2016) SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size. [Online]. Available: https://arxiv.org/abs/1602.07360v4. Accessed 17 Jan 2022

  26. Karadağ B, Arı A, Karadağ M (2021) Derin Öğrenme Modellerinin Sinirsel Stil Aktarımı Performanslarının Karşılaştırılması. J Polytech 0900:2–14. https://doi.org/10.2339/politeknik.885838

    Article  Google Scholar 

  27. Kaya U, Yılmaz A, Dikmen Y (2019) Deep learning methods used in the field of health. Eur J Sci Technol 16:792–808. https://doi.org/10.31590/ejosat.573248

    Article  Google Scholar 

  28. Keleş A (2018) Deep learning and applications in health. J Turkish Stud 13(21):113–127. https://doi.org/10.7827/turkishstudies.14189

    Article  Google Scholar 

  29. Knobloch E (1981) Chaos in the segmented disc dynamo. Phys Lett A 82(9):439–440. https://doi.org/10.1016/0375-9601(81)90274-7

    Article  MathSciNet  Google Scholar 

  30. Krizhevsky A, Sutskever I, Hinton GE (2017) ImageNet classification with deep convolutional neural networks. Commun ACM 60(6):84–90. https://doi.org/10.1145/3065386

    Article  Google Scholar 

  31. Küçük D et al (2018) A literature study on deep learning applications in natural language processing. Int J Manag Inf Syst Comput Sci 2(2):76–86

    Google Scholar 

  32. Kuremoto T, Obayashi M, Kobayashi K, Hirata T, Mabu S (2014) Forecast chaotic time series data by DBNs. In: Proceedings - 2014 7th international congress on image and signal processing, CISP 2014, pp 1130–1135. https://doi.org/10.1109/CISP.2014.7003950

    Chapter  Google Scholar 

  33. Le Cun Y et al (1990) Handwritten Digit Recognition: Applications of Neural Net Chips and Automatic Learning. In: Neurocomputing. Berlin, Heidelberg: Springer Berlin Heidelberg, pp 303–318

  34. LeCun Y, Bottou L, Bengio Y, Haffner P (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2323. https://doi.org/10.1109/5.726791

    Article  Google Scholar 

  35. Lecun Y et al (2018) Model-driven deep-learning. Natl Sci Rev 5(1):22–24. https://doi.org/10.1093/nsr/nwx099

    Article  Google Scholar 

  36. Letellier C, Dutertre P, Maheu B (1995) Unstable periodic orbits and templates of the Rössler system: toward a systematic topological characterization. Chaos 5(1):271–282. https://doi.org/10.1063/1.166076

    Article  Google Scholar 

  37. Li Y, Lv C (2020) SS-YOLO: an object detection algorithm based on YOLOv3 and ShuffleNet. In: 2020 IEEE 4th information technology, networking, electronic and automation control conference (ITNEC), Jun. 2020, pp 769–772. https://doi.org/10.1109/ITNEC48623.2020.9085091

    Chapter  Google Scholar 

  38. Liang X, Qi G (2017) Mechanical analysis of Chen chaotic system. Chaos Solit Fractals 98:173–177. https://doi.org/10.1016/j.chaos.2017.03.021

    Article  MathSciNet  Google Scholar 

  39. Lin W, Hung K-W Contention resolution in the loop-augmented ShuffleNet multihop lightwave network. In: 1994 IEEE GLOBECOM. communications: the global bridge, Dec. 2002, pp 186–190. https://doi.org/10.1109/glocom.1994.513404

  40. Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20(2):130–141. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2

    Article  MathSciNet  Google Scholar 

  41. Lu X, Wang W, Ma C, Shen J, Shao L, Porikli F (2019) See more, know more: unsupervised video object segmentation with co-attention siamese networks. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol 2019-June, pp 3618–3627. https://doi.org/10.1109/CVPR.2019.00374

    Chapter  Google Scholar 

  42. Lu S, Lu Z, Zhang Y-D (2019) Pathological brain detection based on AlexNet and transfer learning. J Comput Sci 30:41–47. https://doi.org/10.1016/j.jocs.2018.11.008

    Article  Google Scholar 

  43. Lu X, Wang W, Shen J, Crandall D, Luo J (2022) Zero-shot video object segmentation with co-attention Siamese networks. IEEE Trans Pattern Anal Mach Intell 44(4):2228–2242. https://doi.org/10.1109/TPAMI.2020.3040258

    Article  Google Scholar 

  44. Lu X, Wang W, Shen J, Crandall DJ, Van Gool L (2022) Segmenting objects from relational visual data. IEEE Trans Pattern Anal Mach Intell 44(11):7885–7897. https://doi.org/10.1109/TPAMI.2021.3115815

    Article  Google Scholar 

  45. Pchelintsev AN (2014) Numerical and physical modeling of the dynamics of the Lorenz system. Numer Anal Appl 7(2):159–167. https://doi.org/10.1134/S1995423914020098

    Article  MathSciNet  Google Scholar 

  46. Qian Y, Bi M, Tan T, Yu K (2016) Very deep convolutional neural networks for noise robust speech recognition. IEEE/ACM Trans Audio Speech Lang Process 24(12):2263–2276. https://doi.org/10.1109/TASLP.2016.2602884

    Article  Google Scholar 

  47. Rakhlin A, Shvets A, Iglovikov V, Kalinin AA (2018) Deep convolutional neural networks for breast cancer histology image analysis. In: Lecture Notes in Computer Science, vol 10882 LNCS, pp 737–744. https://doi.org/10.1007/978-3-319-93000-8_83

    Chapter  Google Scholar 

  48. Ravi D et al (2017) Deep learning for health informatics. IEEE J Biomed Heal Informatics 21(1):4–21. https://doi.org/10.1109/JBHI.2016.2636665

    Article  Google Scholar 

  49. Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398. https://doi.org/10.1016/0375-9601(76)90101-8

    Article  Google Scholar 

  50. Russakovsky O et al (2015) ImageNet large scale visual recognition challenge. Int J Comput Vis 115(3):211–252. https://doi.org/10.1007/s11263-015-0816-y

    Article  MathSciNet  Google Scholar 

  51. Sangiorgio M, Dercole F (2020) Robustness of LSTM neural networks for multi-step forecasting of chaotic time series. Chaos Solit Fractals 139:110045. https://doi.org/10.1016/j.chaos.2020.110045

    Article  MathSciNet  Google Scholar 

  52. Szegedy C et al (2015) Going deeper with convolutions. In: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Jun. 2015, vol. 07–12-June, pp 1–9. https://doi.org/10.1109/CVPR.2015.7298594

    Chapter  Google Scholar 

  53. Talo M (2019) Classification of histopathological breast Cancer images using convolutional neural networks. Fırat Üniversitesi Mühendislik Bilim. Derg. 31(2):391–398. https://doi.org/10.35234/fumbd.517939

    Article  MathSciNet  Google Scholar 

  54. Toğaçar M, Ergen B, Özyurt F (2020) Classification of flower species by using feature selection methods in convolutional neural network models. Fırat Üniversitesi Mühendislik Bilim Derg:37–45. https://doi.org/10.35234/fumbd.573630

  55. Toraman S (2018) Pedestrian detection with deep learning from unmanned aerial imagery. J Aviat 2(2):64–69. https://doi.org/10.30518/jav.450913

    Article  Google Scholar 

  56. Wen L, Li X, Li X, Gao L (2019) A new transfer learning based on VGG-19 network for fault diagnosis. In: Proceedings of the 2019 IEEE 23rd international conference on computer supported cooperative work in design, CSCWD 2019, May 2019, pp 205–209. https://doi.org/10.1109/CSCWD.2019.8791884

    Chapter  Google Scholar 

  57. Yeo K (2017) Model-free prediction of noisy chaotic time series by deep learning. https://doi.org/10.48550/arXiv.1710.01693

  58. Yilmaz F, Kose O, Demir A (2019) Comparison of two different deep learning architectures on breast cancer. In: TIPTEKNO 2019 - Tip Teknolojileri Kongresi, Oct. 2019, vol. 2019-Janua, pp 1–4. https://doi.org/10.1109/TIPTEKNO47231.2019.8972042

    Chapter  Google Scholar 

  59. Young T, Hazarika D, Poria S, Cambria E (2018) Recent trends in deep learning based natural language processing. IEEE Comput Intell Mag 13(3):55–75. https://doi.org/10.1109/MCI.2018.2840738

    Article  Google Scholar 

  60. Zhang Z (2021) ResNet-Based model for autonomous vehicles trajectory prediction. In: 2021 IEEE International Conference on Consumer Electronics and Computer Engineering, ICCECE 2021, Jan. 2021, pp 565–568. https://doi.org/10.1109/ICCECE51280.2021.9342418

    Chapter  Google Scholar 

  61. Zhang Y et al (2016) Towards end-to-end speech recognition with deep convolutional neural networks. In: Proceedings of the Annual Conference of the International Speech Communication Association, INTERSPEECH, Sep. 2016, vol. 08–12-Sept, pp 410–414. https://doi.org/10.21437/Interspeech.2016-1446

  62. Zhang X, Zhou X, Lin M, Sun J (2018) ShuffleNet: an extremely efficient convolutional neural network for mobile devices. In: Proceedings of the IEEE computer society conference on computer vision and pattern recognition, pp 6848–6856. https://doi.org/10.1109/CVPR.2018.00716

    Chapter  Google Scholar 

  63. Zhang K, Guo Y, Wang X, Yuan J, Ding Q (2019) Multiple feature reweight DenseNet for image classification. IEEE Access 7:9872–9880. https://doi.org/10.1109/ACCESS.2018.2890127

    Article  Google Scholar 

  64. Zhi W, Gao L, Zhu Z (2020) Garbage classification and recognition based on SqueezeNet. In: Proceedings - 2020 3rd world conference on mechanical engineering and intelligent manufacturing, WCMEIM 2020, Dec. 2020, pp 122–125. https://doi.org/10.1109/WCMEIM52463.2020.00032

    Chapter  Google Scholar 

  65. Zhu Z, Li J, Zhuo L, Zhang J (2017) Extreme weather recognition using a novel fine-tuning strategy and optimized GoogLeNet. In: 2017 International conference on digital image computing: techniques and applications (DICTA), vol. 2017-Decem, pp 1–7. https://doi.org/10.1109/DICTA.2017.8227431

    Chapter  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

  2. Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University of Applied Sciences, 54050, Sakarya, Turkey

    Sezgin Kaçar & Burak Arıcıoğlu

Authors
  1. Süleyman UZUN
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sezgin Kaçar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Burak Arıcıoğlu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S. UZUN, S. KAÇAR and B. ARICIOĞLU contributed to the design and implementation of the research, to the analysis of the results and to the writing of the manuscript.

Corresponding author

Correspondence to Süleyman UZUN.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

UZUN, S., Kaçar, S. & Arıcıoğlu, B. Deep learning based classification of time series of chaotic systems over graphic images. Multimed Tools Appl 83, 8413–8437 (2024). https://doi.org/10.1007/s11042-023-15944-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-15944-3

Keywords

Search

Navigation