Quantifying time series complexity by multi-scale transition network approaches

Complex network approaches for nonlinear time series analysis are still under fast developments. In this work, we propose a set of entropy measures to characterize the multi-scale transition networks which are constructed from nonlinear time series. These entropy measures compare the distances between an empirical distribution P to a uniform distribution P_e, which are achieved via the multi-scale node transition matrix from different perspectives of out-link transitions, and in-link transitions, respectively. In addition, the entropy measures show convergence to zeros for white noise while non-zero values for deterministic chaotic processes. In correlated stochastic processes, the convergence rates are influenced by the correlation length. We show that entropy measures based on transition complexity are able to capture different dynamical states, i.e., tracking routes to chaos and dynamical hysteresis. In the experimental EEG analysis, we show that epileptic brain states are successfully distinguished from healthy control by all entropy measures.