Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions

Kraemer, K. Hauke; Donner, Reik V.; Heitzig, Jobst; Marwan, Norbert

doi:10.1063/1.5024914

Cited by 71 publications

(50 citation statements)

References 30 publications

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“…It should be noted that the CCNDs derived from different time series tended to saturate for the high-dimensional recurrence network. This is because higher-dimensional recurrence networks change fewer and fewer of the distance values between the nodes [ 24 ], which was also observed in numerical investigations associated with the false nearest neighbor method [ 32 ]. In addition, the saturation behavior observed was also partially the result of the finite sample size.…”

Section: Analysis Of Synthetic Datamentioning

confidence: 98%

“…Several strategies for the selection of the threshold have been proposed. It was suggested that choosing a fixed link density is helpful for the estimation of the dynamical properties in many systems [ 23 , 24 , 25 ]. Therefore, we determined the threshold for the L -dimensional recurrence network, Δ L , by setting a fixed link density, ρ L , which is defined as follows:

…”

Section: Network Construction From Time Seriesmentioning

confidence: 99%

See 1 more Smart Citation

A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics

Yang

Zhang

2019

Entropy

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In this paper, a novel analysis method based on recurrence networks is proposed to characterize the evolution of dynamical systems. Through phase space reconstruction, a time series was transformed into a high-dimensional recurrence network and a corresponding low-dimensional recurrence network, respectively. Then, two appropriate statistics, the correlation coefficient of node degrees (CCND) and the edge similarity, were proposed to unravel the evolution properties of the considered signal. Through the investigation of the time series with distinct dynamics, different patterns in the decline rate of the CCND at different network dimensions were observed. Interestingly, an exponential scaling emerged in the CCND analysis for the chaotic time series. Moreover, it was demonstrated that the edge similarity can further characterize dynamical systems and provide detailed information on the studied time series. A method based on the fluctuation of edge similarities for neighboring edge groups was proposed to determine the number of groups that the edges should be partitioned into. Through the analysis of chaotic series corrupted by noise, it was demonstrated that both the CCND and edge similarity derived from different time series are robust under additive noise. Finally, the application of the proposed method to ventricular time series showed its effectiveness in differentiating healthy subjects from ventricular tachycardia (VT) patients.

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Section: Analysis Of Synthetic Datamentioning

confidence: 98%

…”

Section: Network Construction From Time Seriesmentioning

confidence: 99%

A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics

Yang

Zhang

2019

Entropy

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“…Although in the literature, many approaches have been proposed for the selection of m and τ (Fraser, 1986;Albano et al, 1987;Kennel et al, 1992;Kaplan, 1993; Chun-Hua and Xin-Bao, 2004), we computed embedding dimension, m, as the first minimum of the false nearest neighbors function over the possible dimensions from zero to ten. An embedding dimension of m = 4 was obtained (Stephen et al, 2009;Kraemer et al, 2018) (see Figure 5 as en example of the m computation). Furthermore, Time delay τ was computed as the first minimum of the mutual information profile, maximizing the independence among the components of the embedding vector (see Figure 6 as an example of the τ computation).…”

Section: Phase-space (Ps) and Phase Space Reconstructionmentioning

confidence: 99%

Nonlinear Analysis of Eye-Tracking Information for Motor Imagery Assessments

et al. 2020

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This study investigates the assessment of motor imagery (MI) ability in humans. Commonly, MI ability is measured through two methodologies: a self-administered questionnaire (MIQ-3) and the mental chronometry (MC), which measures the temporal discrepancy between the actual and the imagined motor tasks. However, both measures rely on subjects' self-assessment and do not use physiological measures. In this study, we propose a novel set of features extracted from the nonlinear dynamics of the eye gaze signal to discriminate between good and bad imagers. To this aim, we designed an experiment where twenty volunteers, categorized as good or bad imagers according to MC, performed three tasks: a motor task (MT), a visual Imagery task (VI), and a kinaesthetic Imagery task (KI). Throughout the experiment, the subjects' eye gaze was continuously monitored using an eye-tracking system. Eye gaze time series were analyzed through recurrence quantification analysis of the reconstructed phase space and compared between the two groups. Statistical results have shown how nonlinear eye behavior can express an inner dynamics of imagery mental process and may be used as a more objective and physiological-based measure of MI ability.

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“…The similarity threshold, ǫ, is a parameter that determines whether vectors in the phase space are identified as recurrent, i.e., as revisiting the same area of the phase space. Choosing an appropriate value for ǫ can be difficult [34] and investigating the impact of ǫ on RQA output is an active research topic [35,36]; in the present work, we use a nearest neighbor approach that does not require an explicit ǫ to be set.…”

Section: Jrqamentioning

confidence: 99%

Comparison of Cross-Correlation and Joint-Recurrence Quantification Analysis Based Methods for Estimating Coupling Strength in Non-linear Systems

Tolston

Funke

Shockley

2020

Front. Appl. Math. Stat.

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Time-delay stability (TDS) analysis is a method for quantifying interactions in multivariate systems by identifying stable temporal relationships in time series data [1]. This method has been used to create network representations of complex systems. As originally presented, the TDS method relies on cross-correlation-a linear analysis that is restricted to estimating relationships between unidimensional time series, and which, by itself, often does not adequately characterize interactions between many non-linear complex systems of theoretical and practical interest. Thus, modifying TDS so that it relies on joint recurrence quantification analysis (JRQA), an intrinsically non-linear multidimensional framework, and then comparing the ability of the two approaches to detect interactions in non-linear systems is an important task. In the present work, we first show how TDS can be extended using JRQA, a method which is capable of multidimensional assessment of relationships in non-linear systems. In our application of JRQA, we introduce a modification in the form of a weighting factor that accounts for the truncation of time series that results from time-delayed JRQA. We also modify TDS by correcting for a bias in the method and show how analogs of recurrence-based metrics can also be obtained for TDS. We evaluate how TDS results obtained with JRQA compare to those obtained with cross-correlation for known dynamics of coupled non-linear oscillators and from unknown dynamics of multivariate behavioral signals measured from dyads performing a joint problem-solving task. We conclude that TDS using cross-correlation provides results that are comparable to those obtained with JRQA at a much-reduced computational cost.

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Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions

Cited by 71 publications

References 30 publications

A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics

A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics

Nonlinear Analysis of Eye-Tracking Information for Motor Imagery Assessments

Comparison of Cross-Correlation and Joint-Recurrence Quantification Analysis Based Methods for Estimating Coupling Strength in Non-linear Systems

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