TY  - JOUR
A1  - Wendi, Dadiyorto
A1  - Marwan, Norbert
A1  - Merz, Bruno
T1  - In Search of Determinism-Sensitive Region to Avoid Artefacts in Recurrence Plots
JF  - International journal of bifurcation and chaos : in applied sciences and engineering
N2  - As an effort to reduce parameter uncertainties in constructing recurrence plots, and in particular to avoid potential artefacts, this paper presents a technique to derive artefact-safe region of parameter sets. This technique exploits both deterministic (incl. chaos) and stochastic signal characteristics of recurrence quantification (i.e. diagonal structures). It is useful when the evaluated signal is known to be deterministic. This study focuses on the recurrence plot generated from the reconstructed phase space in order to represent many real application scenarios when not all variables to describe a system are available (data scarcity). The technique involves random shuffling of the original signal to destroy its original deterministic characteristics. Its purpose is to evaluate whether the determinism values of the original and the shuffled signal remain closely together, and therefore suggesting that the recurrence plot might comprise artefacts. The use of such determinism-sensitive region shall be accompanied by standard embedding optimization approaches, e.g. using indices like false nearest neighbor and mutual information, to result in a more reliable recurrence plot parameterization.
KW  - Recurrence plot
KW  - phase space time delay embedding reconstruction
KW  - artefact avoidance
Y1  - 2017
U6  - https://doi.org/10.1142/S0218127418500074
SN  - 0218-1274
SN  - 1793-6551
VL  - 28
IS  - 1
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Wendi, Dadiyorto
A1  - Marwan, Norbert
T1  - Extended recurrence plot and quantification for noisy continuous dynamical systems
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - One main challenge in constructing a reliable recurrence plot (RP) and, hence, its quantification [recurrence quantification analysis (RQA)] of a continuous dynamical system is the induced noise that is commonly found in observation time series. This induced noise is known to cause disrupted and deviated diagonal lines despite the known deterministic features and, hence, biases the diagonal line based RQA measures and can lead to misleading conclusions. Although discontinuous lines can be further connected by increasing the recurrence threshold, such an approach triggers thick lines in the plot. However, thick lines also influence the RQA measures by artificially increasing the number of diagonals and the length of vertical lines [e.g., Determinism (DET) and Laminarity (LAM) become artificially higher]. To take on this challenge, an extended RQA approach for accounting disrupted and deviated diagonal lines is proposed. The approach uses the concept of a sliding diagonal window with minimal window size that tolerates the mentioned deviated lines and also considers a specified minimal lag between points as connected. This is meant to derive a similar determinism indicator for noisy signal where conventional RQA fails to capture. Additionally, an extended local minima approach to construct RP is also proposed to further reduce artificial block structures and vertical lines that potentially increase the associated RQA like LAM. The methodology and applicability of the extended local minima approach and DET equivalent measure are presented and discussed, respectively.
Y1  - 2018
U6  - https://doi.org/10.1063/1.5025485
SN  - 1054-1500
SN  - 1089-7682
VL  - 28
IS  - 8
PB  - American Institute of Physics
CY  - Melville
ER  -