TY  - JOUR
A1  - Krämer, Hauke Kai
A1  - Marwan, Norbert
T1  - Border effect corrections for diagonal line based recurrence quantification analysis measures
JF  - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics
N2  - Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.
KW  - Recurrence plots
KW  - Recurrence quantification analysis
KW  - Shannon entropy
KW  - Dynamical invariants
Y1  - 2019
U6  - https://doi.org/10.1016/j.physleta.2019.125977
SN  - 0375-9601
SN  - 1873-2429
VL  - 383
IS  - 34
PB  - Elsevier
CY  - Amsterdam
ER  -