Threshold grouping method to derive complex networks from time series

Abstract

We propose a new method to derive complex networks from time series data. Each data point in the time series is treated as a single node and nodes are connected if their values differ by a value less than a threshold. The method is easy to implement and transforms periodic time series into regular networks, and random time series into random networks. Network specific properties such as scale freeness, small world effects and the presence of hubs are captured by this method. The method converts a chaotic time series into a scale-free network. The method is applied on a model time series (a chaotic time series of Henon map, a periodic time series and a random time series) and an experimental time series (fluctuating pressure time series measured from the combustor involving turbulent flow). The complex network derived from the Henon map obeys a power law degree distribution, highlighting the scale free behavior of the associated chaotic state. The motivation for proposing the present method is that the method is able to convert specific patterns in the dynamics of a time series into spatial structures in the complex network. We show this specialty of the present method by constructing a complex network from a time series of acoustic pressure measured from a combustor involving turbulent flow that exhibits intermittency. The intermittent bursts in the considered time series are converted into clusters in the corresponding complex network.

Keywords: Time series analysis; Complex networks; Threshold grouping method