Manis George, Platakis Dimitrios, Sassi Roberto
Department of Computer Science and Engineering, University of Ioannina, 45500 Ioannina, Greece.
Dipartimento di Informatica, Università degli Studi di Milano, 20133 Milano, Italy.
Entropy (Basel). 2024 Aug 19;26(8):704. doi: 10.3390/e26080704.
Sample entropy embeds time series into m-dimensional spaces and estimates entropy based on the distances between points in these spaces. However, when samples can be considered as missing or invalid, defining distance in the embedding space becomes problematic. Preprocessing techniques, such as deletion or interpolation, can be employed as a solution, producing time series without missing or invalid values. While deletion ignores missing values, interpolation replaces them using approximations based on neighboring points. This paper proposes a novel approach for the computation of sample entropy when values are considered as missing or invalid. The proposed algorithm accommodates points in the m-dimensional space and handles them there. A theoretical and experimental comparison of the proposed algorithm with deletion and interpolation demonstrates several advantages over these other two approaches. Notably, the deviation of the expected sample entropy value for the proposed methodology consistently proves to be lowest one.
样本熵将时间序列嵌入到m维空间中，并基于这些空间中各点之间的距离来估计熵。然而，当样本可被视为缺失或无效时，在嵌入空间中定义距离就会出现问题。诸如删除或插值等预处理技术可作为一种解决方案，生成没有缺失或无效值的时间序列。删除操作忽略缺失值，而插值则基于相邻点的近似值来替换它们。本文提出了一种在值被视为缺失或无效时计算样本熵的新方法。所提出的算法在m维空间中容纳各点并在其中进行处理。将所提出的算法与删除和插值方法进行理论和实验比较，结果表明该算法相对于其他两种方法具有若干优势。值得注意的是，所提出方法的预期样本熵值的偏差始终被证明是最低的。
