Xu Meng, Shang Pengjian, Qi Yue, Zhang Sheng
Department of Mathematics, School of Science, Beijing Jiaotong University, No.3 of Shangyuan Residence, Haidian District, Beijing 100044, China.
School of Environment and Natural Resources, Renmin University of China, Beijing 100872, China.
Chaos. 2019 May;29(5):053108. doi: 10.1063/1.5045121.
This paper addresses a novel multiscale fractional order distribution entropy based on a similarity matrix (MFS-DistEn) approach to quantify the information of time series on multiple time scales. It improves the metric method of distance matrix in the original DistEn algorithm and further defines the similarity degree between each vector so that we could measure the probability density distribution more accurately. Besides, the multiscale distribution entropy based on similarity matrix combines the advantages of both the multiscale analysis and DistEn and is able to identify dynamical and scale-dependent information. Inspired by the properties of Fractional Calculus, we select the MFS-DistEn notation as the main indicator to present the relevant properties. The characteristics of the generalized MFS-DistEn are tested in both simulated nonlinear signals generated by the autoregressive fractionally integrated moving-average process, logistic map, and real world data series. The results demonstrate the superior performance of the new algorithm and reveal that tuning the fractional order allows a high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The improved similarity DistEn still has relatively lower sensitivity to the predetermined parameters and decreases with an increase of scale.
本文提出了一种基于相似性矩阵的新型多尺度分数阶分布熵（MFS-DistEn）方法，用于量化多时间尺度上时间序列的信息。它改进了原始DistEn算法中距离矩阵的度量方法，并进一步定义了各向量之间的相似程度，从而能够更准确地度量概率密度分布。此外，基于相似性矩阵的多尺度分布熵结合了多尺度分析和DistEn的优点，能够识别动态的、依赖尺度的信息。受分数阶微积分性质的启发，我们选择MFS-DistEn作为主要指标来呈现相关特性。在自回归分数整合移动平均过程、逻辑斯谛映射生成的模拟非线性信号以及实际数据序列中测试了广义MFS-DistEn的特性。结果证明了新算法的优越性能，并表明调整分数阶可使算法对信号演化具有高灵敏度，这在描述复杂系统的动力学方面很有用。改进后的相似性DistEn对预定参数的灵敏度仍然相对较低，且随着尺度的增加而降低。
