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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Alternate Entropy Computations by Applying Recurrence Matrix Masking.

Charles L Webber1

  • 1Department of Cell and Molecular Physiology, Health Sciences Campus, Loyola University Chicago, 2160 South First Avenue, Maywood, IL 60153, USA.

Entropy (Basel, Switzerland)
|January 21, 2022
PubMed
Summary
This summary is machine-generated.

Tilting recurrence plot boundaries minimizes line entropy by truncating diagonal lines to identical lengths. This study investigates the impact of this novel approach on other recurrence variables in dynamical systems analysis.

Keywords:
line entropynonlinear dynamicsrecurrence matrix maskingrecurrence quantifications

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Area of Science:

  • Dynamical systems theory
  • Nonlinear time series analysis
  • Recurrence quantification analysis (RQA)

Background:

  • Recurrence plots and their quantifications are typically limited by signal truncation within a triangular area.
  • Truncation effects can influence recurrence variables, varying with the dynamical system.
  • Line entropy maximization in periodic systems, due to varied line element truncation, prompted this research.

Purpose of the Study:

  • To investigate the effect of tilting recurrence plot boundaries on recurrence variables.
  • To compare recurrence variables computed using a standard triangular area versus a 45-degree tilted box area.
  • To understand new truncation influences imposed by the tilted box method.

Main Methods:

  • Redefining the recurrence plot area to a 45-degree tilted box.
  • Comparing recurrence variables computed with the triangular versus the boxed recurrence area.
  • Analyzing mathematical, real-world, and toy series data, including the logistic equation, Dow Jones Industrial Average, and a square wave pulse.

Main Results:

  • Minimizing line entropy to 0.000 bits/bin by truncating diagonal lines to identical lengths within the tilted box.
  • Most recurrence variables showed good agreement in timing and amplitude between the triangular and boxed areas.
  • Some recurrence variables exhibited differences, indicating new truncation influences.

Conclusions:

  • The tilted box method offers a novel way to analyze recurrence in dynamical systems by altering truncation effects.
  • This approach significantly impacts line entropy and introduces specific influences on other recurrence variables.
  • Further investigation is needed to fully understand the implications for various dynamical systems and data types.