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A Recurrence Plot-Based Distance Measure

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Translational Recurrences

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 103))

Abstract

Given a set of time series, our goal is to identify prototypes that cover the maximum possible amount of occurring subsequences regardless of their order. This scenario appears in the context of the automotive industry, where the goal is to determine operational profiles that comprise frequently recurring driving behavior patterns. This problem can be solved by clustering, however, standard distance measures such as the dynamic time warping distance might not be suitable for this task, because they aim at capturing the cost of aligning two time series rather than rewarding pairwise recurring patterns. In this contribution, we propose a novel time series distance measure, based on the notion of recurrence plots, which enables us to determine the (dis)similarity of multivariate time series that contain segments of similar trajectories at arbitrary positions. We use recurrence quantification analysis to measure the structures observed in recurrence plots and to investigate dynamical properties, such as determinism, which reflect the pairwise (dis)similarity of time series. In experiments on real-life test drives from Volkswagen, we demonstrate that clustering multivariate time series using the proposed recurrence plot-based distance measure results in prototypical test drives that cover significantly more recurring patterns than using the same clustering algorithm with dynamic time warping distance.

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Acknowledgments

The proposed recurrence plot-based distance measure for clustering multivariate time series was developed in cooperation with the Volkswagen AG, Wolfsburg. Thanks to Bernd Werther and Matthias Pries for their contribution of expert knowledge and their help in recording vehicular sensor data.

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Authors and Affiliations

  1. DAI Laboratory, Berlin Institute of Technology, Ernst-Reuter-Platz 7, 10587, Berlin, Germany

    Stephan Spiegel, Johannes-Brijnesh Jain & Sahin Albayrak

Authors
  1. Stephan Spiegel
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  2. Johannes-Brijnesh Jain
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  3. Sahin Albayrak
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Corresponding author

Correspondence to Stephan Spiegel .

Editor information

Editors and Affiliations

  1. Potsdam Institute for Climate Impact Res, Potsdam, Germany

    Norbert Marwan

  2. Dept. of Psychology, University of Cincinnati, Cincinnati, Ohio, USA

    Michael Riley

  3. Istituto Superiore di Sanita, Rome, Italy

    Alessandro Giuliani

  4. Loyola University Chicago, Stritch School of Medicine, Health Sciences Division,Dept. of Cell and Molecular Physiology, Maywood, Illinois, USA

    Charles L. Webber, Jr.

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Spiegel, S., Jain, JB., Albayrak, S. (2014). A Recurrence Plot-Based Distance Measure. In: Marwan, N., Riley, M., Giuliani, A., Webber, Jr., C. (eds) Translational Recurrences. Springer Proceedings in Mathematics & Statistics, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-09531-8_1

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