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Characterizing unstructured data with the nearest neighbor permutation entropy.

Leonardo G J M Voltarelli1, Arthur A B Pessa1, Luciano Zunino2,3

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Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

We introduce k-nearest neighbor permutation entropy, a novel method for analyzing complex unstructured data. This physics-inspired technique enhances pattern detection and offers superior noise resilience for diverse datasets.

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Area of Science:

  • Complex Systems Analysis
  • Information Theory
  • Data Science

Background:

  • Permutation entropy is a powerful physics-inspired tool for analyzing complex datasets.
  • Current applications are mainly limited to structured data like time series and images.
  • A need exists for methods applicable to unstructured, high-dimensional data.

Purpose of the Study:

  • To introduce k-nearest neighbor permutation entropy (kNN-PE) for analyzing unstructured data.
  • To demonstrate kNN-PE's ability to identify patterns in data regardless of configuration or dimensionality.
  • To enhance the capabilities of ordinal methods for broader data analysis.

Main Methods:

  • Constructing k-nearest neighbor graphs to define data relationships.
  • Employing random walks on these graphs to extract ordinal patterns.
  • Calculating kNN-PE based on the distribution of these ordinal patterns.

Main Results:

  • kNN-PE accurately identifies variations in unstructured data patterns.
  • The method surpasses conventional measures like spatial autocorrelation in precision.
  • kNN-PE naturally incorporates amplitude and time gap information, improving noise resilience.

Conclusions:

  • kNN-PE significantly expands the applicability of ordinal methods to unstructured data.
  • This innovation enhances pattern analysis for complex, high-dimensional datasets.
  • Opens new research avenues for permutation entropy in diverse data types.