Article

The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 13-22

First online:

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

  • Yoshito HirataAffiliated withAihara Complexity Modelling Project, ERATOInstitute of Industrial Science, The University of Tokyo Email author 
  • , Shunsuke HoraiAffiliated withAihara Complexity Modelling Project, ERATOInstitute of Industrial Science, The University of Tokyo
  • , Kazuyuki AiharaAffiliated withAihara Complexity Modelling Project, ERATOInstitute of Industrial Science, The University of Tokyo

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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.