基于对角线的递归量化分析测量的边界效应校正
Border effect corrections for diagonal line based recurrence quantification analysis measures
摘要：
递归量化分析（RQA）定义了许多基于递归图（RP）中对角线结构的量化器。由于RP的有限大小，这些线可以被RP的边界切割，从而使对角线的长度分布偏置，从而使基于线的RQA测量偏置。在这封信中，我们调查的影响所提到的边界效应和增厚的对角线在RP（由切向运动引起）的对角线长度分布的估计，量化的熵。虽然理论上预期与李雅普诺夫谱的关系，但在许多研究中，所提到的熵产生了矛盾的结果。在这里，我们总结了修正方案，边界效应和切向运动，并系统地比较它们的方法从文献中。我们表明，这些修正导致预期的行为的对角线长度熵，特别是意味着零值的情况下，一个正常的运动和正值的混沌运动。此外，我们测试这些方法在噪声条件下，为了应用统计研究提供实用的工具。
英文摘要：
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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