Reproduction of distance matrices and original time series from recurrence plots and their applicationsYoshito Hirata1, 2, Shunsuke Horai1, 2 and Kazuyuki Aihara1, 2
1 Aihara Complexity Modelling Project, ERATO, JST, Japan
2 Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
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.
© EDP Sciences, Springer-Verlag 2008