IEEE Trans Biomed Eng. 2019 Mar;66(3):623-631. doi: 10.1109/TBME.2018.2852713. Epub 2018 Jul 3.
Traditional definition of sample entropy (SampEn), here referred to as global SampEn (GSampEn), provides a conditional entropy estimate that blurs the local statistical properties of the time series. We hypothesized that a local version of SampEn (LSampEn) might be more powerful in the presence of determinism than GSampEn.
LSampEn was computed by calculating the probability of the current sample conditioned on each reference pattern and averaging it over all reference patterns. The improved ability of LSampEn compared to GSampEn was demonstrated by simulating deterministic periodic, deterministic chaotic, and linear stochastic dynamics corrupted by additive noise and over real cardiovascular variability series recorded from 16 healthy subjects (max-min age range: 22-58 years) during incremental bicycle ergometer exercise.
We found that: i) LSampEn is more robust in describing deterministic periodic or nonlinear features in the presence of additive noise than GSampEn, ii) in association with a surrogate approach, LSampEn is more powerful in detecting nonlinear dynamics than GSampEn, iii) LSampEn and GSampEn are equivalent in the presence of stochastic linear dynamics, and iv) only LSampEn can detect the decrease of complexity of heart period variability during bicycle exercise being a likely hallmark of sympathetic activation.
LSampEn preserves the GSampEn capability in characterizing the complexity of short sequences but improves its reliability in the presence of deterministic patterns featuring sharp state transitions and nonlinear dynamics.
Variations of complexity can be measured with a greater statistical power over short series using LSampEn, especially when nonlinear features are present.
这里提到的传统样本熵（SampEn）定义，即全局 SampEn（GSampEn），提供了一个条件熵估计，模糊了时间序列的局部统计特性。我们假设 SampEn 的局部版本（LSampEn）在存在确定性时可能比 GSampEn 更强大。
LSampEn 通过计算当前样本相对于每个参考模式的概率并对所有参考模式进行平均来计算。通过模拟确定性周期性、确定性混沌和线性随机动力学，并添加噪声污染以及来自 16 名健康受试者（最大-最小年龄范围：22-58 岁）在递增自行车测力计运动期间记录的真实心血管变异性系列，证明了 LSampEn 与 GSampEn 相比具有提高的能力。
我们发现：i）LSampEn 在存在加性噪声时比 GSampEn 更能稳健地描述确定性周期性或非线性特征，ii）与替代方法结合，LSampEn 在检测非线性动力学方面比 GSampEn 更强大，iii）在存在随机线性动力学时，LSampEn 和 GSampEn 是等效的，iv）只有 LSampEn 可以检测到自行车运动期间心率变异性复杂性的降低，这可能是交感神经激活的标志。
LSampEn 保留了 GSampEn 对短序列复杂性特征的能力，但提高了其在存在具有急剧状态转换和非线性动力学的确定性模式时的可靠性。
使用 LSampEn 可以在短序列上以更大的统计功效测量复杂度的变化，尤其是在存在非线性特征时。
