Centered and Averaged Fuzzy Entropy to Improve Fuzzy Entropy Precision

Area of Science:

• Time series analysis
• Biomedical signal processing
• Entropy measures

Background:

• Approximate entropy, sample entropy, and fuzzy entropy (FuzzyEn) are common for time series analysis.
• Standard FuzzyEn's precision is limited by signal length, which is often short in real applications.
• Existing methods struggle with precision when analyzing limited data.

Purpose of the Study:

• To introduce a novel FuzzyEn measure with enhanced precision for time series analysis.
• To overcome the limitations of standard FuzzyEn concerning data length and pattern comparison.
• To improve the accuracy of entropy-based analysis in biomedical and synthetic signals.

Main Methods:

• Developed a centered and averaged FuzzyEn by increasing sample numbers without altering time series length.
• Incorporated reflected, inversed, and glide-reflected patterns beyond simple translations.
• Applied the new measure to synthetic and biomedical time series data for validation.

Main Results:

• The centered and averaged FuzzyEn demonstrated superior precision compared to standard FuzzyEn.
• Relative percentile range was reduced, indicating more robust and reliable entropy estimations.
• The new method outperformed standard sample entropy and fuzzy entropy measures.

Conclusions:

• The centered and averaged FuzzyEn offers a more precise and reliable method for time series analysis, especially with limited data.
• This enhanced measure effectively handles various pattern transformations, improving analytical capabilities.
• Further research can explore its application and comparison with other entropy measures across diverse fields.