TY  - JOUR
A1  - Krämer, Hauke Kai
A1  - Donner, Reik Volker
A1  - Heitzig, Jobst
A1  - Marwan, Norbert
T1  - Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - 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.
Recurrence plots (RPs) provide an intuitive tool for visualizing the (potentially multi-dimensional) trajectory of a dynamical system in state space. In case only univariate observations of the system’s overall state are available, time-delay embedding has become a standard procedure for qualitatively reconstructing the dynamics in state space. The selection of a threshold distance 𝜀
, which distinguishes close from distant pairs of (reconstructed) state vectors, is known to have a substantial impact on the recurrence plot and its quantitative characteristics, but its corresponding interplay with the embedding dimension has not yet been explicitly addressed. Here, we point out that the results of recurrence quantification analysis (RQA) and related methods are qualitatively robust under changes of the (sufficiently high) embedding dimension only if the full distribution of pairwise distances between state vectors is considered for selecting 𝜀, which is achieved by consideration of a fixed recurrence rate.
Y1  - 2018
U6  - https://doi.org/10.1063/1.5024914
SN  - 1054-1500
SN  - 1089-7682
VL  - 28
IS  - 8
PB  - American Institute of Physics
CY  - Melville
ER  -