多尺度多变量模糊熵分析

多尺度多变量样本熵评价同步多通道数据的多变量复杂度, 是非线性动态相互关系的一种反映, 但其统计稳定性差, 且不适用于非线性非平稳信号. 研究利用模糊隶属度函数代替模式相似判断的硬阈值准则, 并分析模糊隶属度函数形式的影响; 研究利用多变量经验模态分解算法进行多尺度化, 并对比其处理效果. 仿真试验表明, 模糊隶属度函数的引入可以有效提高算法的统计稳定性, 所构造的物理模糊隶属度函数的性能最为显著; 基于多变量经验模态分解算法的多尺度化过程可更有效地捕获信号的不同尺度成分, 从而更敏感地区分具有不同复杂度的信号. 对临床试验数据的分析支持以上结论, 且结果提示随着年龄增加或心脏疾病的发生, 心率变异性和心脏舒张间期变异性的多变量复杂度以不同的方式降低: 年龄增加会使低尺度熵值降低, 表示近程相关性的丢失; 而心脏疾病会同时影响各个尺度的熵值, 即同时丢失了近程和长时相关性. 该结论可用于指导心血管疾病的无创预警研究.关键词：多变量复杂度多尺度多变量模糊熵物理模糊隶属度函数多变量经验模态分解

Multiscale multivariate fuzzy entropy analysis

Multiscale multivariate sample entropy can test the multivariate complexity, which is accepted as a kind of reflection of nonlinear dynamical interactions in multichannel data. It is however relatively unstable due to the rigid ranking scheme used in comparison among different patterns. It is not applicable to the nonlinear and non-stationary data because the multiscale framework used is in fact handled by moving average succeeded by down-sampling, which actually has a premise of stationary data. We substitute a fuzzy membership function for the original rigid one and compare the performances of different kinds of fuzzy membership functions. In addition, we employ the multivariate empirical mode decomposition (MEMD) to capture different scales. Results show that the substitution of fuzzy membership function brings in significant stability. It is much more obvious by using the introduced physical fuzzy membership function (PFMF). Also MEMD could capture scales more robustly. In conclusion, the introduced PFMF- and MEMD-based MMFE perform best. Final analysis on the interactions between heart rate variability (HRV) and heart diastolic time interval variability (DIV) validates it. In addition, the results show that the multivariate complexity between HRV and DIV decreases in aging or heart failure group but in a distinctly different decreasing manner–it deceased at low scales with aging, indicating a loss of short-range correlation but both at low and high scales with heart failure, which shows the losses of both short- and long-range correlations. Studies in noninvasive detection of cardiovascular diseases should benefit from the above conclusions.
Keywords：multivariate complexitymultiscale multivariate fuzzy entropyphysical fuzzy membership functionmultivariate empirical mode decomposition