Complexity and Disorder of 1/f(α) Noises

The complexity and the disorder of a 1/ [Formula: see text] 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/ [Formula: see text] noises of various values of [Formula: see text] exhibits a distinct inverted U curve. For the 1/ [Formula: see text] noises, we have shown that [Formula: see text] decreases monotonically as AE increases, which indicates that [Formula: see text] is also a measure of disorder. Furthermore, a 1/ [Formula: see text] noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1/ [Formula: see text] noises for [Formula: see text] around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at [Formula: see text] = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at [Formula: see text] = 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 [Formula: see text] , while it is 0.73 when using spectral-analysis-based [Formula: see text].