A complex network approach to characterize clustering of events in irregular time series

TL;DR

This paper introduces a novel complex network framework to analyze the clustering of events in irregular time series, enabling detailed insights into local dynamics and individual clusters beyond global measures.

Contribution

It presents a new network-based method for analyzing event clustering, incorporating community detection to identify and study individual clusters in irregular time series.

Findings

Effective characterization of event clustering in diverse systems

Application to turbulent flow droplet arrivals and ECG signals

Reveals local interaction patterns and time scales

Abstract

In complex systems, events occur at irregular intervals that inherently encode the underlying dynamics of the system. Analyzing the temporal clustering of these events reveals critical insights into the non-random patterns and the temporal evolution. Existing techniques can effectively quantify the overall clustering tendency of events using global statistical measures. However, these macroscopic approaches leave a critical gap, as they do not attempt to investigate the dynamics of individual clusters. Analyzing individual clusters is essential, as it helps comprehend the local interactions that actively drive the system dynamics, which may be obscured by global averaging, while simultaneously revealing the time scales involved. To address these limitations, we propose a complex network-based framework for analyzing clustering of events occurring at irregular intervals. The framework establishes connections using arrival times, transforming the time series into a network. Network properties are then used to quantify the clustering. Further, a community detection algorithm is used to identify individual clusters in time series. We illustrate the method by applying it to standard arrival processes, such as the Poisson process and the Markov-modulated Poisson process. To further demonstrate its scope, we apply the method to two diverse systems: the time series of droplet arrivals in turbulent flows and the R-R intervals in electrocardiogram (ECG) signals.