Entropy-based analysis provides powerful tools for quantifying the complexity and irregularity of time series data without requiring signal decomposition or transformation. These methods enable effective characterization of temporal patterns across diverse domains including power quality monitoring, vibration analysis, biomedical signal processing, financial forecasting, and environmental data analysis.

Core Entropy Algorithms

Seven fundamental entropy measures form the foundation for comprehensive time series analysis:

Approximate Entropy Family

• Approximate Entropy (ApEn)
• Multiscale Approximate Entropy (MSE-ApEn)
• Hierarchical Approximate Entropy (H-ApEn)
• Composite Multiscale Approximate Entropy (CMSE-ApEn)
• Refined Composite Multiscale Approximate Entropy (RCMSE-ApEn)
• Time-Shift Multiscale Approximate Entropy (TSMSE-ApEn)

Sample Entropy Family

• Sample Entropy (SampEn)
• Multiscale Sample Entropy (MSE-SampEn)
• Hierarchical Sample Entropy (H-SampEn)
• Composite Multiscale Sample Entropy (CMSE-SampEn)
• Refined Composite Multiscale Sample Entropy (RCMSE-SampEn)
• Time-Shift Multiscale Sample Entropy (TSMSE-SampEn)

Fuzzy Entropy Family

• Fuzzy Entropy (FuzEn)
• Multiscale Fuzzy Entropy (MSE-FuzEn)
• Hierarchical Fuzzy Entropy (H-FuzEn)
• Composite Multiscale Fuzzy Entropy (CMSE-FuzEn)
• Refined Composite Multiscale Fuzzy Entropy (RCMSE-FuzEn)
• Time-Shift Multiscale Fuzzy Entropy (TSMSE-FuzEn)

Distribution Entropy Family

• Distribution Entropy (DistEn)
• Multiscale Distribution Entropy (MSE-DistEn)
• Hierarchical Distribution Entropy (H-DistEn)
• Composite Multiscale Distribution Entropy (CMSE-DistEn)
• Refined Composite Multiscale Distribution Entropy (RCMSE-DistEn)
• Time-Shift Multiscale Distribution Entropy (TSMSE-DistEn)

Permutation Entropy Family

• Permutation Entropy (PermEn)
• Multiscale Permutation Entropy (MSE-PermEn)
• Hierarchical Premutation Entropy (H-PermEn)
• Composite Multiscale Permutation Entropy (CMSE-PermEn)
• Refined Composite Multiscale Permutation Entropy (RCMSE-PermEn)
• Time-Shift Multiscale Permutation Entropy (TSMSE-PermEn)

Weighted Permutatino Entropy Family

• Weighted Permutation Entropy (WPE)
• Multiscale Weighted Permutation Entropy (MSE-WPE)
• Hierarchical Weighted Permutation Entropy (H-WPE)
• Composite Multiscale Weighted Permutation Entropy (CMSE-WPE)
• Refined Composite Multiscale Weighted Permutation Entropy (RCMSE-WPE)
• Time-Shift Multiscale Weighted Permutation Entropy (TSMSE-WPE)

Dispersion Entropy Family

• Dispersion Entropy (DispEn)
• Multiscale Dispersion Entropy (MSE-DispEn)
• Hieracrhical Dispersion Entropy (H-DispEn)
• Composite Multiscale Dispersion Entropy (CMSE-DispEn)
• Refined Composite Multiscale Dispersion Entropy (RCMSE-DispEn)
• Time-Shift Multiscale Dispersion Entropy (TSMSE-DispEn)