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Using the Information Provided by Forbidden Ordinal Patterns in Permutation Entropy to Reinforce Time Series

David Cuesta-Frau1

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Summary
This summary is machine-generated.

This study introduces a new Shannon Entropy normalization for permutation entropy (PE), enhancing its ability to classify time series data. The improved method shows greater discriminating power and accuracy across diverse datasets.

Keywords:
forbidden patternsordinal patternspermutation entropysignal classification

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Area of Science:

  • Complexity Science
  • Time Series Analysis
  • Information Theory

Background:

  • Permutation Entropy (PE) is a useful tool for time series analysis but has limitations.
  • Existing weaknesses include ignoring amplitude information, sensitivity to equal values, and parameter dependence.
  • A key challenge is the limited discriminating power of entropy measures for data classification.

Purpose of the Study:

  • To improve the class discriminating power of permutation entropy for time series classification.
  • To introduce and evaluate a novel Shannon Entropy normalization scheme for PE.
  • To compare the performance of the proposed method against the standard PE algorithm.

Main Methods:

  • Standard permutation entropy (PE) was applied to various time series datasets for classification.
  • A new normalization scheme was proposed: dividing relative frequencies by the number of observed ordinal patterns.
  • The classification accuracy and discriminating power of the new method were compared to standard PE.

Main Results:

  • The proposed Shannon Entropy normalization scheme demonstrated higher class discriminating power than standard PE.
  • The new method achieved significant differences in six out of seven datasets, compared to four for standard PE.
  • Improved classification accuracy was observed using the enhanced PE method.

Conclusions:

  • The novel normalization scheme effectively enhances the discriminating power of permutation entropy.
  • Incorporating information on the number of found patterns improves classification performance.
  • The proposed algorithm is easily implemented and offers a significant advancement over classical PE normalization.