Hard c-mean transition network method for analysis of time series

Abstract

Transition network is a powerful tool to analyze nonlinear dynamic characteristics of complex systems, which characterizes the temporal transition property. Few, if any, existing approaches map different time series into transition networks with the same size so that temporal information of time series can be captured more effectively by network measures including typical average node degree, average path length, and so on. To construct a fixed size transition network, the proposed approach uses the embedding dimension method to reconstruct phase space from time series and divides state vectors into different nodes based on the hard c-mean clustering algorithm. The links are determined by the temporal succession of nodes. Our novel method is illustrated by three case studies: distinction of different dynamic behaviors, detection of parameter perturbation of dynamical system, and identification of seismic airgun based on sound data recorded in central Atlantic Ocean. The results show that our proposed method shows good performance in capturing the underlying nonlinear and nonstationary dynamics from short and noisy time series.