Key Laboratory of Ocean Acoustics and Sensing (Northwestern Polytechnical University), Ministry of Industry and Information Technology, 710072 Xi'an, Shaanxi, China.
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China.
Chaos. 2023 Jun 1;33(6). doi: 10.1063/5.0150205.
Entropy, as a nonlinear feature in information science, has drawn much attention for time series analysis. Entropy features have been used to measure the complexity behavior of time series. However, traditional entropy methods mainly focus on one-dimensional time series originating from single-channel transducers and are incapable of handling the multidimensional time series from multi-channel transducers. Previously, the multivariate multiscale sample entropy (MMSE) algorithm was introduced for multi-channel data analysis. Although MMSE generalizes multiscale sample entropy and provides a new method for multidimensional data analysis, it lacks necessary theoretical support and has shortcomings, such as missing cross-channel correlation information and having biased estimation results. This paper proposes an improved multivariate multiscale sample entropy (IMMSE) algorithm to overcome these shortcomings. This paper highlights the existing shortcomings in MMSE under the generalized algorithm. The rationality of IMMSE is theoretically proven using probability theory. Simulations and real-world data analysis have shown that IMMSE is capable of effectively extracting cross-channel correlation information and demonstrating robustness in practical applications. Moreover, it provides theoretical support for generalizing single-channel entropy methods to multi-channel situations.
熵作为信息科学中的一种非线性特征，已经引起了时间序列分析领域的广泛关注。熵特征已被用于测量时间序列的复杂行为。然而，传统的熵方法主要集中在一维时间序列上，这些时间序列来源于单通道传感器，无法处理来自多通道传感器的多维时间序列。先前，提出了多变量多尺度样本熵（MMSE）算法，用于多通道数据分析。虽然 MMSE 推广了多尺度样本熵，并为多维数据分析提供了一种新方法，但它缺乏必要的理论支持，存在一些缺点，例如缺少跨通道相关信息，并且估计结果存在偏差。本文提出了一种改进的多变量多尺度样本熵（IMMSE）算法来克服这些缺点。本文重点讨论了广义算法下 MMSE 存在的不足。通过概率论从理论上证明了 IMMSE 的合理性。模拟和实际数据分析表明，IMMSE 能够有效地提取跨通道相关信息，在实际应用中具有稳健性。此外，它为将单通道熵方法推广到多通道情况提供了理论支持。
