title: Scale-dependent intrinsic entropies of complex time series.
abstract: Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal's complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.
authors.affiliation: Research Center for Adaptive Data Analysis and Center for Dynamical Biomarkers and Translational Medicine, National Central University, Taoyuan, Taiwan, Republic of China.
authors.forename: Jia-Rong
authors.initials: JR
authors.lastname: Yeh
authors.affiliation: Research Center for Adaptive Data Analysis and Center for Dynamical Biomarkers and Translational Medicine, National Central University, Taoyuan, Taiwan, Republic of China Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center/Harvard Medical School, Boston, MA, USA chungkang.peng@gmail.com.
authors.forename: Chung-Kang
authors.initials: CK
authors.lastname: Peng
authors.affiliation: Research Center for Adaptive Data Analysis and Center for Dynamical Biomarkers and Translational Medicine, National Central University, Taoyuan, Taiwan, Republic of China.
authors.forename: Norden E
authors.initials: NE
authors.lastname: Huang
mesh_terms: D000328:Adult; D000368:Aged; D000465:Algorithms; D004562:Electrocardiography; D019277:Entropy; D017709:Fractals; D006333:Heart Failure / Q000503:physiopathology; D006339:Heart Rate / Q000502:physiology; D006801:Humans; D008875:Middle Aged; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors
keywords: complexity; detrending; empirical mode decomposition; fractal property; multi-scale entropy