Castiglioni Paolo, Żurek Sebastian, Piskorski Jaroslaw, Kośmider Marcin, Guzik Przemyslaw, Cè Emiliano, Rampichini Susanna, Merati Giampiero
Annu Int Conf IEEE Eng Med Biol Soc. 2013;2013:5053-6. doi: 10.1109/EMBC.2013.6610684.
Sample Entropy (SampEn) is a popular method for assessing the unpredictability of biological signals. Its calculation requires to preliminarily set the tolerance threshold r and the embedding dimension m. Even if most studies select m=2 and r=0.2 times the signal standard deviation, this choice is somewhat arbitrary. Effects of different r and m values on SampEn have been rarely assessed, because of the high computational burden of this task. Recently, however, a fast algorithm for estimating correlation sums (Norm Component Matrix, NCM) has been proposed that allows calculating SampEn quickly over wide ranges of r and m. The aim of our work is to describe the structure of SampEn of physiological signals with different complex dynamics as a function of m and r and in relation to the correlation sum. In particular, we investigate whether the criterion of "maximum entropy" for selecting r previously proposed for Approximate Entropy, also applies to SampEn; and whether information from correlation sums provides indications for the choice of r and m. For this aim we applied the NCM algorithm on electromyographic and mechanomyographic signals during isometric muscle contraction, estimating SampEn over wide ranges of r (0.01 ≤ r ≤ 5) and m (from 1 to 11). Results indicate that the "maximum entropy" criterion to select r in Approximate Entropy cannot be applied to SampEn. However, the analysis of correlation sums alternatively suggests to choose r that at any m maximizes the number of "escaping vectors", i.e., data points effectively contributing to the SampEn estimation.
样本熵（SampEn）是一种用于评估生物信号不可预测性的常用方法。其计算需要预先设定容忍阈值r和嵌入维度m。即使大多数研究选择m = 2且r =信号标准差的0.2倍，但这种选择多少有些随意。由于该任务的计算负担较重，不同r和m值对样本熵的影响很少得到评估。然而，最近有人提出了一种用于估计相关和的快速算法（规范分量矩阵，NCM），它能够在r和m的较宽范围内快速计算样本熵。我们工作的目的是描述不同复杂动力学的生理信号的样本熵结构，它是m和r的函数，并与相关和相关。特别是，我们研究先前为近似熵提出的选择r的“最大熵”标准是否也适用于样本熵；以及相关和的信息是否为r和m的选择提供了指示。为此，我们将NCM算法应用于等长肌肉收缩期间的肌电图和机械肌电图信号，在较宽的r范围（0.01≤r≤5）和m范围（从1到11）内估计样本熵。结果表明，在近似熵中选择r的“最大熵”标准不适用于样本熵。然而，相关和的分析则建议选择在任何m值下能使“逃逸向量”数量最大化的r，即对样本熵估计有有效贡献的数据点。
