Reproduction of distance matrices and original time series from recurrence plots and their applications
Reproduction of distance matrices and original time series from recurrence plots and their applications
复制标题
DOI：
10.1140/epjst/e2008-00830-8
复制
发表时间：
2008-10-01
影响因子：
2.8
通讯作者：
Aihara, Kazuyuki
中科院分区：
文献类型：
--
作者：
Hirata, Yoshito;Horai, Shunsuke;Aihara, Kazuyuki
我们提出了一种方法来重现距离矩阵和原始时间序列的递归图。该过程是（i）将递归图转换为加权图，以及（ii）计算该加权图上的每对节点之间的距离。我们通过再现原始时间序列的拓扑形状来证明这种方法。我们还提出了两个应用。第一个应用是从递归图中获得最大李雅普诺夫指数，而不再现原始时间序列的形状。第二个应用是重建一个共同的确定性驱动力从强迫系统的观察。因此，该方法在数据分析中开辟了新的领域。
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.