title: Multiscale entropy analysis of biological signals: a fundamental bi-scaling law.
abstract: Since introduced in early 2000, multiscale entropy (MSE) has found many applications in biosignal analysis, and been extended to multivariate MSE. So far, however, no analytic results for MSE or multivariate MSE have been reported. This has severely limited our basic understanding of MSE. For example, it has not been studied whether MSE estimated using default parameter values and short data set is meaningful or not. Nor is it known whether MSE has any relation with other complexity measures, such as the Hurst parameter, which characterizes the correlation structure of the data. To overcome this limitation, and more importantly, to guide more fruitful applications of MSE in various areas of life sciences, we derive a fundamental bi-scaling law for fractal time series, one for the scale in phase space, the other for the block size used for smoothing. We illustrate the usefulness of the approach by examining two types of physiological data. One is heart rate variability (HRV) data, for the purpose of distinguishing healthy subjects from patients with congestive heart failure, a life-threatening condition. The other is electroencephalogram (EEG) data, for the purpose of distinguishing epileptic seizure EEG from normal healthy EEG.
authors.affiliation: Institute of Complexity Science and Big Data Technology, Guangxi University Nanning, China ; PMB Intelligence LLC Sunnyvale, CA, USA.
authors.forename: Jianbo
authors.initials: J
authors.lastname: Gao
authors.affiliation: PMB Intelligence LLC Sunnyvale, CA, USA.
authors.forename: Jing
authors.initials: J
authors.lastname: Hu
authors.affiliation: Institute of Complexity Science and Big Data Technology, Guangxi University Nanning, China ; School of Management, University of Chinese Academy of Sciences Beijing, China.
authors.forename: Feiyan
authors.initials: F
authors.lastname: Liu
authors.affiliation: Institute of Complexity Science and Big Data Technology, Guangxi University Nanning, China ; PMB Intelligence LLC Sunnyvale, CA, USA.
authors.forename: Yinhe
authors.initials: Y
authors.lastname: Cao
keywords: adaptive filtering; fractal signal; heart rate variability (HRV); multiscale entropy analysis; scaling law