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  Border effect corrections for diagonal line based recurrence quantification analysis measures

Krämer, K.-H., Marwan, N. (2019): Border effect corrections for diagonal line based recurrence quantification analysis measures. - Physics Letters A, 383, 34, 125977.
https://doi.org/10.1016/j.physleta.2019.125977

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Krämer, Kai-Hauke1, Author              
Marwan, Norbert1, Author              
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1Potsdam Institute for Climate Impact Research, ou_persistent13              

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 Abstract: 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.

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 Dates: 2019
 Publication Status: Finally published
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1016/j.physleta.2019.125977
PIKDOMAIN: RD4 - Complexity Science
eDoc: 8625
Research topic keyword: Nonlinear Dynamics
Research topic keyword: Complex Networks
Model / method: Open Source Software
Model / method: Nonlinear Data Analysis
Organisational keyword: RD4 - Complexity Science
Working Group: Development of advanced time series analysis techniques
 Degree: -

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Title: Physics Letters A
Source Genre: Journal, SCI, p3
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Pages: - Volume / Issue: 383 (34) Sequence Number: 125977 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/journals398