Complexity and Disorder of 1/fα 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.

Gait Stability Measurement by Using Average Entropy

“…Figure 4 depicts the plot of the EoE versus the AE values of the 79 SI time series of databases D2 and D3. The comparison of the EoE and AE plot exhibited an inverted U curve [ 21 ], which is another example of a complexity versus disorder inverted U curve for physiologic signals [ 17 , 18 , 24 , 35 ], as expected. We find that a threshold of AE th = 1.06, the dashed line in the figure, is optimal to differentiate the healthy from the diseased.…”

The autonomic balance of heart rhythm complexity after renal artery denervation: insight from entropy of entropy and average entropy analysis

“…AE is the average of local instabilities of a series measured using multi-scale Shannon entropy instead of evaluating the appearance of repetitive patterns of the series. AE has been shown reliable in quantifying the disorders of simulated series with different amplitudes and numbers of shuffled data points [ 22 ] and those of colored noises [ 23 ]. In the heart rate signal analysis, AE has been used to differentiate the healthy, the congestive heart failure (CHF), and the atrial fibrillation (AF) subjects with an accuracy of 94%, higher than those obtained using Shannon entropy and SampEn.…”