Characterizing Complex Spatiotemporal Patterns from Entropy Measures

Area of Science:

• Complex Systems Analysis
• Statistical Thermodynamics
• Time Series Analysis

Background:

• Probabilistic entropy measurements are vital for analyzing complex systems and time series.
• Current entropy methods require further development for two- and three-dimensional data.
• Spatiotemporal process classification remains a challenge.

Purpose of the Study:

• To develop a new method for classifying spatiotemporal processes using entropy measurements.
• To validate the method by distinguishing between five classes of random patterns.
• To identify optimal entropy measures for enhanced classification performance.

Main Methods:

• Selected five classes of random patterns: white noise, red noise, reaction-diffusion, hydrodynamic turbulence, and plasma turbulence (MHD).
• Evaluated seven entropy measurement techniques from matrices.
• Developed a parameter space using the two most effective entropy measures: Shannon permutation entropy (SHp) and Tsallis Spectral Permutation Entropy (Sqs).

Main Results:

• The SHp×Sqs parameter space effectively segregates the five classes of spatiotemporal processes.
• Shannon permutation entropy (SHp) and Tsallis Spectral Permutation Entropy (Sqs) showed superior combined performance.
• Specific sectors within the SHp×Sqs space were identified for each dynamic process class.

Conclusions:

• The proposed entropy-based method offers a robust approach for classifying complex spatiotemporal patterns.
• The SHp×Sqs parameter space provides a powerful tool for distinguishing between different dynamic processes.
• This method can be utilized to train machine learning models for automated spatiotemporal pattern classification.