中文摘要：

样本熵可以有效反映一维时间序列中新模式的生成概率,但缺乏对二维序列复杂度的表征能力.基于对传统样本熵方法的改进,提出一种在振幅-周期二维空间描述波形复杂度的方法,二维样本熵反映了波形振动在振幅-周期空间中新模式的生成概率.通过仿真实验证明了这种方法描述波形复杂度的有效性,当波形的复杂度特征表现为振幅-周期的交互作用时,二维样本熵对复杂度的描述比一维条件下的样本熵更加有效.基于二维样本熵对抑郁症组和对照组的脑电复杂度进行分析,结果表明,抑郁症组在Alpha频段左侧顶区和左侧枕区的二维样本熵显著低于对照组,表明在上述频段和位置,抑郁症患者脑电中新模式的生成概率显著低于正常人,这一特征可能成为抑郁症的潜在生物标记.

英文摘要：

Sample entropy, a complexity measure that quantifies the new pattern generation rate of time series, has been widely applied to physiological signal analysis. It can effectively reflect the pattern complexity of one-dimensional sequences,such as the information contained in amplitude or period features. However, the traditional method usually ignores the interaction between amplitude and period in time series, such as electroencephalogram（EEG） signals. To address this issue, in this study, we propose a new method to describe the pattern complexity of waveform in a two-dimensional space. In this method, the local peaks of the signals are first extracted, and the variation range and the duration time between the adjacent peaks are calculated as the instantaneous amplitude and period. Then the amplitude and period sequences are combined into a two-dimensional sequence to calculate the sample entropy based on the amplitude and period information. In addition, in order to avoid the influence of the different units in the two dimensions, we use the Jaccard distance to measure the similarity of the amplitude-period bi-vectors in the waveforms, which is different from the one-dimensional method. The Jaccard distance is defined as the ratio of the different area to the combined area of two rectangles containing the amplitude-period bi-vectors in the Cartesian coordinate system. To verify the effectiveness of the method, we construct five sets of simulative waveforms in which the numbers of patterns are completely equal in one-dimensional space of amplitude or period but the numbers in two-dimensional space are significantly different（P 〈0.00001）. Simulation results show that the two-dimensional sample entropy could effectively reflect the different complexities of the five signals（P 〈0.00001）, while the sample entropy in one-dimensional space of amplitude or period cannot do. The results indicate that compared with the one-dimensional sample entropy, the two-dimensional sample entropy is very effective to