Complexity and Disorder of 1/f^α Noises

Area of Science:

• Non-linear dynamics
• Physiological signal analysis
• Information theory

Background:

• 1/fα noise is a ubiquitous signal in nature.
• Entropy measures, like entropy of entropy (EoE) and average entropy (AE), are used to quantify time series complexity and disorder.
• Cardiac interbeat (RR) interval series exhibit 1/fα noise characteristics.

Purpose of the Study:

• To introduce EoE and AE as quantitative measures for 1/fα noise complexity and disorder.
• To establish a relationship between the 1/fα exponent (α) and AE.
• To assess the utility of AE-based analysis for classifying cardiac RR interval series and compare it with spectral analysis.

Main Methods:

• Calculating EoE and AE for 1/fα noise time series with varying α.
• Plotting EoE vs. AE to observe patterns.
• Establishing the monotonic relationship between α and AE.
• Comparing AE of 1/fα noise with RR interval series from healthy subjects and patients with atrial fibrillation (AF).
• Classifying RR interval series using AE-based α and spectral-analysis-based α.

Main Results:

• 1/fα noise exhibits a distinct inverted U-shaped curve on an EoE vs. AE plot.
• The exponent α decreases monotonically as AE increases, indicating α as a measure of disorder.
• 1/fα noise with α ≈ 1.5 is equivalent to healthy RR interval series.
• Pink noise (α = 1) is equivalent to AF RR interval series.
• White noise (α = 0) is more disordered than AF RR interval series.
• AE-based α classification achieved a macro-average F-score of 0.93, superior to the 0.73 F-score from spectral analysis.

Conclusions:

• AE provides a robust measure of disorder in 1/fα noise and cardiac RR interval series.
• AE-based α offers a more effective method for classifying cardiac rhythm abnormalities compared to spectral analysis.
• This approach offers a novel perspective on analyzing physiological time series.