Complexity and Disorder of 1/<i>f</i>^α Noises

Abstract

The complexity and the disorder of a 1/fα noise time series are quantified by entropy of entropy (EoE) and average entropy (AE), respectively. The resulting EoE vs. AE plot of a series of 1/fα noises of various values of α exhibits a distinct inverted U curve. For the 1/fα noises, we have shown that α decreases monotonically as AE increases, which indicates that α is also a measure of disorder. Furthermore, a 1/fα noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1/fα noises for α around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at α = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at α = 0 is more disordered than AF RR interval series. These results, based on AE, are different from the previous ones based on spectral analysis. The testing macro-average F-score is 0.93 when classifying the RR interval series of three groups using AE-based α, while it is 0.73 when using spectral-analysis-based α.

Keywords

• 1/<i>f^α</i> noises
• power law
• complexity
• disorder
• inverted U curve
• heart rate variability