Permutation entropy: Influence of amplitude information on time series classification performance

Area of Science:

• Time series analysis
• Complexity science
• Signal processing

Background:

• Permutation Entropy (PE) is a widely used complexity measure for time series, analyzing ordinal patterns.
• Standard PE's focus on order, not amplitude, may limit its performance in certain applications.
• Existing amplitude-inclusive PE methods lack comprehensive comparative analysis.

Purpose of the Study:

• To evaluate the performance of standard PE and amplitude-included PE methods.
• To compare PE (ordinal patterns) with Sample Entropy (SampEn, amplitude patterns).
• To determine if combining ordinal and amplitude information enhances time series classification.

Main Methods:

• Quantitative performance analysis of standard PE and amplitude-enhanced PE methods.
• Comparative study using diverse time series datasets.
• Evaluation of classification accuracy based on ordinal patterns, amplitude patterns, and their combination.

Main Results:

• Standard PE and SampEn, when used in isolation, showed limitations in classification accuracy.
• Amplitude-included PE methods did not consistently outperform standard PE across all datasets.
• The highest classification accuracy was achieved by methods that simultaneously utilized both ordinal and amplitude patterns.

Conclusions:

• Combining ordinal and amplitude information provides a more robust approach to time series analysis than using either alone.
• The synergy of ordinal and amplitude patterns offers superior performance for signal classification tasks.
• Future research should explore hybrid methods that integrate diverse pattern information for enhanced time series characterization.