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Fast Computation of Recurrences in Long Time Series

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Translational Recurrences

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

Abstract

We present an approach to recurrence quantification analysis (RQA) that allows to process very long time series fast. To do so, it utilizes the paradigm Divide and Recombine. We divide the underlying matrix of a recurrence plot (RP) into sub matrices. The processing of the sub matrices is distributed across multiple graphics processing unit (GPU) devices. GPU devices perform RQA computations very fast since they match the problem very well. The individual results of the sub matrices are recombined into a global RQA solution. To address the specific challenges of subdividing the recurrence matrix, we introduce means of synchronization as well as additional data structures. Outperforming existing implementations dramatically, our GPU implementation of RQA processes time series consisting of \(N\approx \) 1,000,000 data points in about 5 min.

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Acknowledgments

We would like to thank T. Nocke and F.-W. Gerstengarbe for fruitful discussions. We acknowledge support from the Potsdam Research Cluster for Georisk Analysis, Environmental Change and Sustainability (PROGRESS, support code 03IS2191B).

Author information

Authors and Affiliations

  1. German Research Center for GeoSciences GFZ, Berlin, Germany

    Tobias Rawald, Mike Sips & Doris Dransch

  2. Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Norbert Marwan

Authors
  1. Tobias Rawald
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  2. Mike Sips
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  3. Norbert Marwan
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  4. Doris Dransch
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Corresponding author

Correspondence to Tobias Rawald .

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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Rawald, T., Sips, M., Marwan, N., Dransch, D. (2014). Fast Computation of Recurrences in Long Time Series. 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_2

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