Constructing ordinal partition transition networks from multivariate time series

Jiayang Zhang,Ming Tang,Heng Guo,Michael Small,Yong Zou,Jie Zhou

doi:10.1038/s41598-017-08245-x

Abstract

A growing number of algorithms have been proposed to map a scalar time series into ordinal partition transition networks. However, most observable phenomena in the empirical sciences are of a multivariate nature. We construct ordinal partition transition networks for multivariate time series. This approach yields weighted directed networks representing the pattern transition properties of time series in velocity space, which hence provides dynamic insights of the underling system. Furthermore, we propose a measure of entropy to characterize ordinal partition transition dynamics, which is sensitive to capturing the possible local geometric changes of phase space trajectories. We demonstrate the applicability of pattern transition networks to capture phase coherence to non-coherence transitions, and to characterize paths to phase synchronizations. Therefore, we conclude that the ordinal partition transition network approach provides complementary insight to the traditional symbolic analysis of nonlinear multivariate time series.

Highlights

Nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics
For a given embedding dimension Dx, there are a total of Dx! unique ordinal patterns that can possibly occur in a time series, neglecting equality
Given a scalar time series {x(t)} which is produced by a deterministic dynamical system, the order structure of the time series depends on the embedding dimension Dx and time delay τ33, 34

Summary

Introduction

Nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics. A series of systematic investigations of ordinal methods has been conducted in irregularly sampled time series[27,28,29], which shows high potential for studies of experimental observation data from climate sciences[30]. In this method, the first step is to embed a one-dimensional time series into phase space by using techniques from traditional time delay embedding. Missing ordinal patterns might be related to finite time length during the period of observation and correlated stochastic processes, which require some revised methods for the detection of determinism in relatively short noisy data[39,40,41,42,43]. Network properties obtained are sensitive to different system dynamics, which successfully characterize the difference between healthy and patients from EEG data[25, 26]

Methods

Results

Conclusion