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Topological Data Analysis for Time Series Changing Point Detection

  • Vanderlei Miranda
  • Liang ZhaoEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1075)

Abstract

Pattern changing in time series refers to structural variations in time domain, which, in turn, represents transitions between different states. Since the same state (a piece of time series pattern) can be largely varied in detail, therefore, pattern changing detection in time series is still a hard problem. Topological data analysis (TDA) allows a characterization of time-series data obtained from complex dynamical systems. In this paper, we present a pattern changing detection technique based on TDA. Given a time series, the signal is divided in non-overlapped slicing windows. For each window, we calculate the persistent homology, i.e., the associated barcode. From the barcode, some measures, like the average interval size and persistent entropy, are extracted and plotted against the signal duration. The changing points can be revealed by the measures. Experimental results on artificial and real data sets show promising results of the proposed method.

Keywords

Pattern changing detection Time series analysis Topological data analysis Persistent entropy Complex networks 

References

  1. 1.
    Zomorodian, A.J.: Topology for Computing. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  2. 2.
    Cochrane, J.H.: Time series for macroeconomics and finance, pp. 1–136. Springer (1977)Google Scholar
  3. 3.
    Keogh, E., Chu, S., Hart, D., Pazzani, M.: Segmenting time series: a survey and novel approach. In: Data Mining in Time Series Databases, vol. 57, pp. 1–21. World Scientific Publishing Co. Pte. Ltd. (2004)Google Scholar
  4. 4.
    Vlachos, M., Gunopulos, D., Das, G.: Indexing time-series under conditions of noise. In: Data Mining in Time Series Databases, vol. 57, pp. 67–100. World Scientific Publishing Co. Pte. Ltd. (2004)Google Scholar
  5. 5.
    Last, M., Kandel, A., Bunke, H. (eds.): Data Mining in Time Series Databases, vol. 68. World Scientific Publishing Co. Pte. Ltd., Singapore (2004)zbMATHGoogle Scholar
  6. 6.
    Chintakunta, H., Gentimis, T., Gonzalez-Diaz, R., Jimenez, M.-J., Krim, H.: An entropy-based persistence barcode. Pattern Recogn. 48(2), 391–401 (2015)CrossRefGoogle Scholar
  7. 7.
    Shannon, C., Wiever, W.: The Mathematical Theory of Communication, 10th edn. The University of Illinois Press, Urbana (1964)Google Scholar
  8. 8.
    Rucco, M., Castiglione, F., Merelli, E., Pettini, M.: Characterisation of the idiotypic immune network through persistent entropy. In: Battiston, S., De Pellegrini, F., Caldarelli, G., Merelli, E. (eds.) Proceedings of ECCS 2014, pp. 117–128. Springer, Cham (2016)CrossRefGoogle Scholar
  9. 9.
    Piangerelli, M., Rucco, M., Tesei, L., Merelli, E.: Topolnogical classifier for detecting the emergence of epileptic seizures. BMC Res. Notes 11, 392 (2018)CrossRefGoogle Scholar
  10. 10.
    Rucco, M., et al.: A new topological entropy-based approach for measuring similarities among piecewise linear functions. Sig. Process. 134, 130–138 (2017)CrossRefGoogle Scholar
  11. 11.
    Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar
  12. 12.
    Shoeb, A.H.: Application of machine learning to epileptic seizure onset detection and treatment. Ph.D. thesis, Massachusetts Institute of Technology (2009)Google Scholar
  13. 13.
    Goldberger, A.L., et al.: PhysioBank, PhysioToolkit, and PhysioNet. Circulation 101(23), e215–e220 (2000)CrossRefGoogle Scholar
  14. 14.
    Perea, J., Harer, J.: Sliding windows and persistence: an application of topological methods to signal analysis (2013). arXiv:1307.6188 [math, stat]
  15. 15.
    Adams, H., Tausz, A.: JavaPlex, July 2018. http://appliedtopology.github.io/javaplex/. Accessed 30 Dec 2018

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computing and MathematicsUniversity of São Paulo (USP)Ribeirão PretoBrazil

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