Unbiased recurrence plot quantification of chaotic dynamic systems by eliminating sojourn points

Abstract

International audience—Recurrence plots are nonlinear tools used to visual-ize the behavior of trajectories of Dynamic Systems. Occurrence of false points known as 'sojourn points' have biased recurrence plots. To solve this contentious issue, the use of high embedding dimension was proposed. However it required a lot of computa-tion and was based on the phase space. For that, we proposed in this paper to compare four quantification techniques, by dropping out sojourn points from the recurrence test of time series. Firstly, a recurrence plot and embedding of two were used as reference methods. Secondly, the number of points in the pattern used for testing recurrences was increased and a m-pattern recurrence plot was introduced. Thirdly, a single system's output and its corresponding derivative were proposed. Numerical inference showed that it was sufficient to work on a single measurement regardless of the degrees of freedom of the considered system and thus the embedding dimension. The proposed techniques succeeded in eliminating sojourn points. They provided a tool for a clean unbiased recurrence plots which permits better analysis of chaotic dynamic systems

Advanced Discrimination between Healthy and Intrauterine Growth Restricted Fetuses by Unbiased Recurrence Plots

“…The second parameter used is the cross-determinism (% CDET), proposed by our previous work [2,3], as it seems powerful in detecting healthy-distressed FHR transition. % CDET is used to quantify false recurrences also known as sojourn points, which result from oversampling the trajectory of the dynamics of the studied system and appear as lines perpendicular to the Length of Identity (the main diagonal of the plot) in RPs [3,19], and it is defined by:…”

“…Chen et al showed that RQA measures are more accurate than the standard entropy analysis techniques in detecting biomedical time series states [12]. Recurrence Plots introduced in our previous work [2,3] have shown their usefulness in detecting fetal distress due to IUGR. These plots were Unbiased Recurrence Plots (URPs) applied to Fetal Heart Rates (FHRs) in order to (i) validate the performance of the cuttingedge removal of sojourn points, i.e.…”

“…Some of these tools were quantitative, such as the entropy (En) analysis and types including, but not limited to, the approximated entropy, sample entropy, fuzzy entropy and recently n-order entropy [4,5,7,8,11]. Other methods were qualitative such as the Recurrence Plots (RPs) and their corresponding Recurrence Quantification Analysis (RQA) [2,3,10]. Chen et al showed that RQA measures are more accurate than the standard entropy analysis techniques in detecting biomedical time series states [12].…”

“…In Zaylaa et al [2,3] we have validated URPs on the logistic map and a single healthy and a single distressed fetuses. This paper demonstrates the application of URPs to a larger database composed of 50 FHRs (25 H-FHRs and 25 IUGR-FHRs).…”

“…Complexity analysis of fetal heart rate (FHR) recordings are constantly developed to discriminate distressed fetuses due to IUGR. Such complexity techniques have been employed to detect and classify signals into healthy and distressed classes [2][3][4][5][6][7][8][9][10].…”