Sampling effects on recurrence microstates distribution

Abstract

The method of recurrence plots (RP) is a valuable tool in time series analysis. Recurrence microstate analysis is a useful concept, which allows a deep characterization of the time series dynamics. How to sample the microstates and a robust sampling strategy are central questions in recurrence microstate analysis. We study different sampling strategies: with overlapping or not, using the full RP or just half RP. Three time series are employed in our analysis: the uniform random noise, the logistic map and an EEG experimental time series. We compare microstate distributions from the sampling strategies using the Jensen–Shannon distance. In addition, we estimate the recurrence entropy for the analyzed sampling strategies for variable microstate samplings. We conclude that the overlapping sampling shows a superior performance compared to the non-overlapping strategy. This study investigates criteria to determine a robust microstate sampling size by analyzing the asymptotic behavior of recurrence entropy, entropy differences, and the standard deviation of an ensemble time series. Additionally, the Jensen–Shannon distance is combined with recurrence entropy to establish a reliable sampling size, showing that while the optimal sampling size depends on the time series dynamics and microstate size, a rule of thumb for microstates with size $k=3$ is a sample size of around the lower bound of $O\left(10^4\right)$ for most series.