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(Multiscale) Cross-Entropy Methods: A Review.

Antoine Jamin1,2, Anne Humeau-Heurtier2

  • 1COTTOS Médical, Allée du 9 novembre 1989, 49240 Avrillé, France.

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|December 8, 2020
PubMed
Summary

This review summarizes cross-entropy measures for time series analysis. It covers advancements in multiscale approaches for understanding coupled dynamical behaviors across different scales.

Keywords:
asynchronycomplexitycouplingcross-approximate entropycross-conditional entropycross-distribution entropycross-entropycross-fuzzy entropycross-sample entropymultiscale cross-entropy

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Area of Science:

  • Time Series Analysis
  • Information Theory
  • Dynamical Systems

Background:

  • Cross-entropy was developed in 1996 to measure asynchronism between time series.
  • A multiscale cross-entropy measure was introduced in 2009 to analyze coupling behavior across multiple scales.
  • Numerous improvements and alternative methods have emerged since the initial development.

Purpose of the Study:

  • To provide a state-of-the-art review of cross-entropy measures.
  • To highlight advancements in multiscale cross-entropy approaches.
  • To consolidate current knowledge on analyzing time series coupling dynamics.

Main Methods:

  • Literature review of cross-entropy measures.
  • Analysis of multiscale cross-entropy methodologies.
  • Synthesis of recent developments in the field.

Main Results:

  • Cross-entropy is a foundational tool for time series asynchronism.
  • Multiscale approaches enhance the analysis of complex coupling behaviors.
  • The field has seen significant methodological evolution.

Conclusions:

  • Cross-entropy and its multiscale variants are crucial for time series analysis.
  • Continued research has refined these measures for complex systems.
  • This review offers a comprehensive overview of the current landscape.