Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions

TL;DR

This paper proposes a method for selecting recurrence thresholds based on the distribution of pairwise distances in reconstructed state spaces, improving robustness across different embedding dimensions.

Contribution

It introduces an empirical approach to threshold selection using distance distribution percentiles, reducing embedding dimension dependence in recurrence analysis.

Findings

Threshold selection based on distance distribution percentiles is effective.

The method reduces embedding dimension effects on recurrence characteristics.

Numerical tests support the empirical approach's robustness.

Abstract

The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.