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On a topological criterion to select a recurrence threshold.

Ioannis Andreadis1, Athanasios D Fragkou2, Theodoros E Karakasidis2

  • 1International School of The Hague, Wijndaelerduin 1, 2554 BX The Hague, The Netherlands.

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Summary
This summary is machine-generated.

This study introduces a topological criterion to select the optimal recurrence threshold for time series analysis using recurrence plots. This method ensures the stability of recurrence plot structures across varying thresholds, enhancing data interpretation.

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Area of Science:

  • Complex Systems Analysis
  • Nonlinear Dynamics
  • Data Science

Background:

  • Recurrence plots (RPs) are valuable tools for analyzing time series data.
  • Selecting an appropriate recurrence threshold is crucial for accurate RP construction.
  • Existing methods for threshold selection can be sensitive and lack robustness.

Purpose of the Study:

  • To propose a novel topological criterion for optimal recurrence threshold selection.
  • To enhance the robustness and reliability of recurrence plot analysis.
  • To provide a data-driven method for threshold determination in time series.

Main Methods:

  • A metric structure for the set of recurrence plots was defined using recurrence plot deviation distance.
  • A range of threshold values were systematically evaluated to construct corresponding recurrence plots.
  • A topological criterion was applied to identify the threshold yielding a stable RP image.

Main Results:

  • The proposed topological criterion effectively identifies an optimal recurrence threshold.
  • The optimal threshold ensures that the recurrence plot remains structurally similar to plots generated with nearby thresholds.
  • The method demonstrated successful application to both the Lorenz dynamical system and Molecular Dynamic simulations.

Conclusions:

  • The developed topological criterion offers a robust method for recurrence threshold selection.
  • This approach improves the interpretability and reliability of recurrence plot analysis.
  • The findings have significant implications for analyzing complex dynamical systems and simulations.