Generalized Gaussian Distribution Improved Permutation Entropy: A New Measure for Complex Time Series Analysis.

Area of Science:

• Complex systems analysis
• Time series signal processing
• Entropy-based feature extraction

Background:

• Traditional permutation entropy (PE) faces limitations with diverse data distributions and signal characteristics.
• Existing multiscale entropy methods like MPE and MDE struggle with signal separability in complex datasets.

Purpose of the Study:

• To introduce generalized Gaussian distribution improved permutation entropy (GGDIPE) for robust time series analysis.
• To develop a multiscale variant (MGGDIPE) for improved feature extraction from complex signals.
• To evaluate the performance of GGDIPE and MGGDIPE against established entropy algorithms.

Main Methods:

• Data normalization using generalized Gaussian distribution cumulative distribution function.
• Application of improved permutation entropy to preserve signal magnitude and temporal correlations.
• Development and application of a multiscale version (MGGDIPE) for enhanced analysis.
• Comparative analysis with traditional PE, multiscale PE (MPE), and multiscale dispersion entropy (MDE).

Main Results:

• GGDIPE demonstrates reduced sensitivity to parameter variations and strong noise resistance.
• The algorithm accurately reveals chaotic system dynamics and operates faster than PE.
• MGGDIPE shows significantly better separability for RR interval, EEG, bearing fault, and underwater acoustic signals.
• MGGDIPE achieved 97.5% accuracy in underwater target recognition, outperforming MDE (70.5%) and MPE (62.5%).

Conclusions:

• GGDIPE and MGGDIPE offer enhanced capabilities for analyzing complex time series with diverse distributions.
• The proposed methods provide superior performance, robustness, and efficiency compared to existing entropy algorithms.
• MGGDIPE shows exceptional promise for applications in signal processing and pattern recognition, particularly in underwater acoustics.