Border effect corrections for diagonal line based recurrence quantification analysis measures

Kraemer, K. Hauke; Marwan, Norbert

doi:10.1016/j.physleta.2019.125977

Cited by 26 publications

(28 citation statements)

References 39 publications

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“…Because long diagonal lines are necessarily truncated at the borders of the recurrence plot, the question arises how much the truncation effect influences the accuracy of DETERM, DMAX and ENT computations, not to mention the remaining recurrence variables. This is the same question formerly asked by Kraemer and Marwan [ 9 ].…”

Section: Introductionmentioning

confidence: 52%

“…More sophisticated approaches for quantifying recurrence entropy are based on matrix microstates [ 13 ] and categorical time series [ 14 ]. Finally, Kraemer and Marwan [ 9 ] described another method similar to the one introduced in this paper. That is they recomputed entropy by masking the recurrence plot such that the square recurrence matrix was windowed within a diamond pattern overlaying the traditional plot.…”

Section: Disparity Between Recurrence Line Entropy Values and Lyapunov Exponentsmentioning

confidence: 99%

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Alternate Entropy Computations by Applying Recurrence Matrix Masking

Webber

2021

Entropy

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In practicality, recurrence analyses of dynamical systems can only process short sections of signals that may be infinitely long. By necessity, the recurrence plot and its quantifications are constrained within a truncated triangle that clips the signals at its borders. Recurrence variables defined within these confining borders can be influenced more or less by truncation effects depending upon the system under evaluation. In this study, the question being asked is what if the boundary borders were tilted, what would be the effect on all recurrence variables? This question was prompted by the observation that line entropy values are maximized for highly periodic systems in which the infinitely long line elements are truncated to different unique lengths. However, by redefining the recurrence plot area to a 45-degree tilted box within the triangular area, the diagonal lines would consequently be truncated to identical lengths. Such masking would minimize the line entropy to 0.000 bits/bin. However, what new truncation influences would be imposed on the other recurrence variables? This question is examined by comparing recurrence variables computed with the triangular recurrence area versus boxed recurrence area. Examples include the logistic equation (mathematical series), the Dow Jones Industrial Average over a decade (real-word data), and a square wave pulse (toy series). Good agreement among the variables in terms of timing and amplitude was found for most, but not all variables. These important results are discussed.

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Section: Introductionmentioning

confidence: 52%

Section: Disparity Between Recurrence Line Entropy Values and Lyapunov Exponentsmentioning

confidence: 99%

Alternate Entropy Computations by Applying Recurrence Matrix Masking

Webber

2021

Entropy

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“…Including RL in feature selection approaches may also improve the performance of machine learning techniques that classify nonlinear data [72]. Another line of research should be concerned with the robustness of the proposed method against spurious effects introduced by erroneous embedding and RP related pitfalls when compared to traditional RQA measures [44,45].…”

Section: Discussionmentioning

confidence: 99%

“…Line-based recurrence measures have been applied to a diversity of complex real-world systems as complexity measures to uncover transitions [27]. Yet, different embedding parameters can yield varying results and edge effects as well as high sampling rates might result in spurious quantifications [44], thus requiring corrections [45]. On top of that, the application of line-based RQA measures is limited to systems that do not show more complex recurring patterns which are referred to as microstates of an RP [28].…”

Section: Recurrence Analysismentioning

confidence: 99%

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

et al. 2021

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We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.

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“…A special case is periodic dynamics. Due to the boundary effect of the finite-size RP, diagonal lines of periodic dynamics have different length and the corresponding ENT values are higher than that for noise, requesting a border correction schema 32 . However, as we do not expect here periodic dynamics and continuous diagonal lines crossing the RP's border, such correction schema is not necessary in our application.…”

Section: Methodsmentioning

confidence: 99%

Frequency spectrum recurrence analysis

Ladeira

Marwan

Filho

et al. 2020

Sci Rep

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In this paper, we present the new frequency spectrum recurrence analysis technique by means of electro-encephalon signals (EES) analyses. The technique is suitable for time series analysis with noise and disturbances. EES were collected, and alpha waves of the occipital region were analysed by comparing the signals from participants in two states, eyes open and eyes closed. Firstly, EES were characterized and analysed by means of techniques already known to compare with the results of the innovative technique that we present here. We verified that, standard recurrence quantification analysis by means of EES time series cannot statistically distinguish the two states. However, the new frequency spectrum recurrence quantification exhibit quantitatively whether the participants have their eyes open or closed. In sequence, new quantifiers are created for analysing the recurrence concentration on frequency bands. These analyses show that EES with similar frequency spectrum have different recurrence levels revealing different behaviours of the nervous system. The technique can be used to deepen the study on depression, stress, concentration level and other neurological issues and also can be used in any complex system.

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Border effect corrections for diagonal line based recurrence quantification analysis measures

Cited by 26 publications

References 39 publications

Alternate Entropy Computations by Applying Recurrence Matrix Masking

Alternate Entropy Computations by Applying Recurrence Matrix Masking

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

Frequency spectrum recurrence analysis

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