Girault Jean-Marc, Humeau-Heurtier Anne
Groupe ESEO, 49000 Angers, France.
Laboratoire Angevin de Recherche en Ingénierie des Systèmes (LARIS), Univ Angers, 49000 Angers, France.
Entropy (Basel). 2018 Apr 15;20(4):287. doi: 10.3390/e20040287.
Several entropy measures are now widely used to analyze real-world time series. Among them, we can cite approximate entropy, sample entropy and fuzzy entropy (FuzzyEn), the latter one being probably the most efficient among the three. However, FuzzyEn precision depends on the number of samples in the data under study. The longer the signal, the better it is. Nevertheless, long signals are often difficult to obtain in real applications. This is why we herein propose a new FuzzyEn that presents better precision than the standard FuzzyEn. This is performed by increasing the number of samples used in the computation of the entropy measure, without changing the length of the time series. Thus, for the comparisons of the patterns, the mean value is no longer a constraint. Moreover, translated patterns are not the only ones considered: reflected, inversed, and glide-reflected patterns are also taken into account. The new measure (so-called centered and averaged FuzzyEn) is applied to synthetic and biomedical signals. The results show that the centered and averaged FuzzyEn leads to more precise results than the standard FuzzyEn: the relative percentile range is reduced compared to the standard sample entropy and fuzzy entropy measures. The centered and averaged FuzzyEn could now be used in other applications to compare its performances to those of other already-existing entropy measures.
现在有几种熵度量方法被广泛用于分析实际的时间序列。其中，我们可以列举近似熵、样本熵和模糊熵（FuzzyEn），后者可能是这三种方法中最有效的。然而，FuzzyEn的精度取决于所研究数据中的样本数量。信号越长，效果越好。然而，在实际应用中，长信号往往很难获得。这就是为什么我们在此提出一种新的FuzzyEn，它比标准的FuzzyEn具有更高的精度。这是通过增加用于熵度量计算的样本数量来实现的，而不改变时间序列的长度。因此，对于模式的比较，平均值不再是一个限制。此外，平移后的模式不是唯一被考虑的：反射、反转和滑动反射模式也被纳入考虑。新的度量方法（所谓的中心化平均FuzzyEn）被应用于合成信号和生物医学信号。结果表明，中心化平均FuzzyEn比标准FuzzyEn产生更精确的结果：与标准样本熵和模糊熵度量相比，相对百分位数范围减小。现在，中心化平均FuzzyEn可用于其他应用，以将其性能与其他已有的熵度量方法进行比较。
