@article{WendiMarwanMerz2018,
  author    = {Wendi, Dadiyorto and Marwan, Norbert and Merz, Bruno},
  title     = {In Search of Determinism-Sensitive Region to Avoid Artefacts in Recurrence Plots},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {28},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {1},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127418500074},
  pages     = {15},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{WendiMarwan2018,
  author    = {Wendi, Dadiyorto and Marwan, Norbert},
  title     = {Extended recurrence plot and quantification for noisy continuous dynamical systems},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {28},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {8},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5025485},
  pages     = {9},
  year      = {2018},
  abstract  = {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.},
  language  = {en}
}
@article{WendiMerzMarwan2019,
  author    = {Wendi, Dadiyorto and Merz, Bruno and Marwan, Norbert},
  title     = {Assessing hydrograph similarity and rare runoff dynamics by cross recurrence plots},
  series = {Water resources research},
  volume    = {55},
  journal   = {Water resources research},
  number    = {6},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {0043-1397},
  doi       = {10.1029/2018WR024111},
  pages     = {4704 -- 4726},
  year      = {2019},
  abstract  = {This paper introduces a novel measure to assess similarity between event hydrographs. It is based on cross recurrence plots (CRP) and recurrence quantification analysis (RQA), which have recently gained attention in a range of disciplines when dealing with complex systems. The method attempts to quantify the event runoff dynamics and is based on the time delay embedded phase space representation of discharge hydrographs. A phase space trajectory is reconstructed from the event hydrograph, and pairs of hydrographs are compared to each other based on the distance of their phase space trajectories. Time delay embedding allows considering the multidimensional relationships between different points in time within the event. Hence, the temporal succession of discharge values is taken into account, such as the impact of the initial conditions on the runoff event. We provide an introduction to cross recurrence plots and discuss their parameterization. An application example based on flood time series demonstrates how the method can be used to measure the similarity or dissimilarity of events, and how it can be used to detect events with rare runoff dynamics. It is argued that this methods provides a more comprehensive approach to quantify hydrograph similarity compared to conventional hydrological signatures.},
  language  = {en}
}