Characterizing unstructured data with the nearest neighbor permutation entropy

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.