School of Systems Science, Beijing Normal University, Beijing 100875, People's Republic of China.
Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E. 2017 Jun;95(6-1):062114. doi: 10.1103/PhysRevE.95.062114. Epub 2017 Jun 12.
Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.
熵测度广泛应用于量化不同领域中动力系统的复杂性。然而，由于熵测度和估计器的多样性以及现实世界时间序列的复杂性，包括非平稳性和长程相关性 (LRC)，熵方法的实际应用具有挑战性。我们对三种基本测度（熵、条件熵、信息存储）和三种传统估计器（线性、核、最近邻）的性能、偏差和局限性进行了系统研究。我们研究了熵测度对估计器和过程特定参数的依赖性，并通过随机自回归过程的模拟展示了由于伪像（趋势、尖峰、局部方差变化）引起的三种类型非平稳性的影响。我们还分析了长程相关性对熵测度的理论和估计值的影响。最后，我们将熵方法应用于来自不同生理状态和临床条件的受试者的心率变异性数据。我们发现，熵测度只能区分特定类型的心脏动力学变化，并且适当的预处理对于正确的估计和解释至关重要。本工作展示了熵方法的局限性，并阐明了如何减轻偏差并提供对结果的正确解释，可为熵方法的应用和现有研究的评估提供全面的参考。
