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The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 13–22 | Cite as

Reproduction of distance matrices and original time series from recurrence plots and their applications

  • Yoshito HirataEmail author
  • Shunsuke Horai
  • Kazuyuki Aihara
Article

Abstract

We propose a method to reproduce distance matrices and original time series from recurrence plots. The procedure is to (i)convert a recurrence plot to a weighted graph and (ii)calculate a distance between each pair of nodes on this weighted graph. We demonstrate this method by reproducing the topological shape of original time series. We also propose two applications. The first application is to obtain the maximal Lyapunov exponent from a recurrence plot without reproducing the shapes of original time series. The second application is to reconstruct a common deterministic driving force from observations of forced systems. Thus, the method opens new fields in data analysis.

Keywords

Time Series European Physical Journal Special Topic Multidimensional Scaling Spike Train Time Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2008

Authors and Affiliations

  • Yoshito Hirata
    • 1
    • 2
    Email author
  • Shunsuke Horai
    • 1
    • 2
  • Kazuyuki Aihara
    • 1
    • 2
  1. 1.Aihara Complexity Modelling Project, ERATOJSTJapan
  2. 2.Institute of Industrial Science, The University of TokyoTokyoJapan

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