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Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications.

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  • 1Technological Institute of Informatics, Universitat Politècnica de València, Alcoi Campus, 03801 Alcoi, Spain.

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Summary
This summary is machine-generated.

Shorter time series lengths than previously thought are sufficient for stable Permutation Entropy (PE) calculations. Even very short series allow robust classification, challenging the need for excessively long data.

Keywords:
embedded dimensionpermutation entropyrelevance analysisshort time recordssignal classification

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Area of Science:

  • Time Series Analysis
  • Complexity Science
  • Biomedical Signal Processing

Background:

  • Permutation Entropy (PE) is a vital time series complexity measure, widely applied in medicine.
  • PE calculation typically requires time series length (N), embedded dimension (m), and delay (τ).
  • Existing guidelines for parameter selection are general, lacking specific recommendations for optimal N, m, and τ.

Purpose of the Study:

  • To investigate the practical implications of the N >> m! rule for Permutation Entropy.
  • To analyze how Permutation Entropy varies with series length (N) and embedded dimension (m).
  • To evaluate classification performance using PE with varying N and m across diverse datasets.

Main Methods:

  • Analysis of Permutation Entropy variations across synthetic (random, spikes, logistic) and real-world (climatology, seismic, financial, biomedical) time series.
  • Systematic variation of time series length (N) and embedded dimension (m) to assess their impact on PE.
  • Classification performance assessment using PE-derived features with different N and m values.

Main Results:

  • Shorter time series lengths than suggested by N >> m! are adequate for stable PE calculation.
  • Robust classification is achievable with very short time series using PE measurements.
  • Differences among time series classes become apparent even at minimal lengths.

Conclusions:

  • The N >> m! guideline for Permutation Entropy may be overly stringent.
  • Shorter time series lengths offer a viable alternative for stable PE computation and effective classification.
  • The inherent properties of time series, such as forbidden patterns, facilitate early differentiation between classes.