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.

中文翻译：

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1/fα 噪声的复杂性和紊乱

1/fα 噪声时间序列的复杂性和无序度分别由熵的熵 (EoE) 和平均熵 (AE) 量化。由此产生的 EoE 与 AE 曲线的一系列 1/fα 噪声的不同 α 值表现出明显的倒 U 曲线。对于 1/fα 噪声，我们已经证明 α 随着 AE 的增加单调减小，这表明 α 也是无序的度量。此外，1/fα 噪声和心脏搏动 (RR) 间期序列被认为是等效的，因为它们具有相同的 AE。因此，我们发现 α 大约 1.5 的 1/fα 噪声相当于健康受试者的 RR 间隔系列。α = 1 处的粉红噪声等效于心房颤动 (AF) RR 间期系列，而 α = 0 处的白噪声比 AF RR 间期系列更无序。这些结果，基于 AE，与以前基于光谱分析的不同。使用基于 AE 的 α 对三组的 RR 间隔系列进行分类时，测试宏观平均 F 分数为 0.93，而使用基于谱分析的 α 时为 0.73。