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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Zomorodian, A.J.: Topology for Computing. Cambridge University Press, Cambridge (2005)
Cochrane, J.H.: Time series for macroeconomics and finance, pp. 1–136. Springer (1977)
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)
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)
Last, M., Kandel, A., Bunke, H. (eds.): Data Mining in Time Series Databases, vol. 68. World Scientific Publishing Co. Pte. Ltd., Singapore (2004)
Chintakunta, H., Gentimis, T., Gonzalez-Diaz, R., Jimenez, M.-J., Krim, H.: An entropy-based persistence barcode. Pattern Recogn. 48(2), 391–401 (2015)
Shannon, C., Wiever, W.: The Mathematical Theory of Communication, 10th edn. The University of Illinois Press, Urbana (1964)
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)
Piangerelli, M., Rucco, M., Tesei, L., Merelli, E.: Topolnogical classifier for detecting the emergence of epileptic seizures. BMC Res. Notes 11, 392 (2018)
Rucco, M., et al.: A new topological entropy-based approach for measuring similarities among piecewise linear functions. Sig. Process. 134, 130–138 (2017)
Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2002)
Shoeb, A.H.: Application of machine learning to epileptic seizure onset detection and treatment. Ph.D. thesis, Massachusetts Institute of Technology (2009)
Goldberger, A.L., et al.: PhysioBank, PhysioToolkit, and PhysioNet. Circulation 101(23), e215–e220 (2000)
Perea, J., Harer, J.: Sliding windows and persistence: an application of topological methods to signal analysis (2013). arXiv:1307.6188 [math, stat]
Adams, H., Tausz, A.: JavaPlex, July 2018. http://appliedtopology.github.io/javaplex/. Accessed 30 Dec 2018
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Miranda, V., Zhao, L. (2020). Topological Data Analysis for Time Series Changing Point Detection. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1075. Springer, Cham. https://doi.org/10.1007/978-3-030-32591-6_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-32591-6_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32590-9
Online ISBN: 978-3-030-32591-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)