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Summary
This summary is machine-generated.

This study introduces a new metric to find similarities in time series data across different scales. The permutation Jensen-Shannon distance method effectively identifies ordinal patterns in complex systems.

Keywords:
Jensen–Shannon divergencechaotic semiconductor laserdelayed optical feedbackmultiscale analysisordinal patternsordinal similaritypermutation Jensen–Shannon distancepermutation entropysymbolic analysistime series

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Area of Science:

  • Data Science
  • Complex Systems Analysis
  • Time Series Analysis

Background:

  • Time series data analysis is crucial in many scientific fields.
  • Identifying similarities across multiple temporal scales remains a challenge.
  • Existing methods may not capture ordinal patterns effectively.

Purpose of the Study:

  • To implement and validate the permutation Jensen-Shannon distance for time series analysis.
  • To assess the method's capability in discerning ordinal patterns and similarities across temporal scales.
  • To demonstrate the practical application of this metric in a complex photonic system.

Main Methods:

  • Numerical analysis to validate multiscale capabilities.
  • Application of the permutation Jensen-Shannon distance to time series data.
  • Comparative analysis of time series patterns at different temporal resolutions.

Main Results:

  • The permutation Jensen-Shannon distance effectively identifies ordinal similarities between time series.
  • The method's multiscale capabilities were numerically validated.
  • Successful application demonstrated in a complex photonic system, highlighting practical utility.

Conclusions:

  • The permutation Jensen-Shannon distance is a robust tool for analyzing time series data.
  • This metric precisely identifies temporal scales of ordinal similarity.
  • The approach holds broad applicability across diverse scientific disciplines for time series analysis.