Żurek Sebastian, Grabowski Waldemar, Wojtiuk Klaudia, Szewczak Dorota, Guzik Przemysław, Piskorski Jarosław
Institute of Physics, University of Zielona Gora, 65-417 Zielona Gora, Poland.
Department of Cardiology-Intensive Therapy, Poznan University of Medical Sciences Poznan, 61-701 Poznan, Poland.
Entropy (Basel). 2020 Jun 21;22(6):694. doi: 10.3390/e22060694.
Relative consistency is a notion related to entropic parameters, most notably to Approximate Entropy and Sample Entropy. It is a central characteristic assumed for e.g., biomedical and economic time series, since it allows the comparison between different time series at a single value of the threshold parameter . There is no formal proof for this property, yet it is generally accepted that it is true. Relative consistency in both Approximate Entropy and Sample entropy was first tested with the M I X process. In the seminal paper by Richman and Moorman, it was shown that Approximate Entropy lacked the property for cases in which Sample Entropy did not. In the present paper, we show that relative consistency is not preserved for M I X processes if enough noise is added, yet it is preserved for another process for which we define a sum of a sinusoidal and a stochastic element, no matter how much noise is present. The analysis presented in this paper is only possible because of the existence of the very fast NCM algorithm for calculating correlation sums and thus also Sample Entropy.
相对一致性是一个与熵参数相关的概念，最显著的是与近似熵和样本熵相关。它是例如生物医学和经济时间序列所假定的一个核心特征，因为它允许在阈值参数的单个值下对不同时间序列进行比较。虽然没有关于此属性的形式证明，但人们普遍认为它是成立的。近似熵和样本熵中的相对一致性最初是用MIX过程进行测试的。在Richman和Moorman的开创性论文中表明，在样本熵不缺乏该属性的情况下，近似熵却缺乏该属性。在本文中，我们表明，如果添加足够的噪声，MIX过程的相对一致性无法保持，但对于我们定义为正弦和随机元素之和的另一个过程，无论存在多少噪声，相对一致性都能保持。本文所呈现的分析之所以可行，只是因为存在用于计算相关总和以及样本熵的非常快速的NCM算法。
