Fine-grained permutation entropy as a measure of natural complexity for time series
Liu Xiao-Feng(刘小峰)a)b)† and Wang Yue(王越)a)
a The Key Laboratory of Robot and Intelligent Technology of Shandong Province, and College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China; b Institute of Artificial Intelligence and Robot, Xi'an Jiaotong University, Xi'an 710049, China
Abstract In a recent paper [2002 Phys. Rev. Lett.88 174102], Bandt and Pompe propose permutation entropy (PE) as a natural complexity measure for arbitrary time series which may be stationary or nonstationary, deterministic or stochastic. Their method is based on a comparison of neighbouring values. This paper further develops PE, and proposes the concept of fine-grained PE (FGPE) defined by the order pattern and magnitude of the difference between neighbouring values. This measure excludes the case where vectors with a distinct appearance are mistakenly mapped onto the same permutation type, and consequently FGPE becomes more sensitive to the dynamical change of time series than does PE, according to our simulation and experimental results.
Received: 10 November 2008
Revised: 11 January 2009
Accepted manuscript online:
Fund: Project supported by the National High
Technology Research and Development Program of China (Grant No
2007AA04Z238) and the Qingdao Foundation for Development of Science
and Technology, China (Grant
No 06-2-2-10-JCH).
Cite this article:
Liu Xiao-Feng(刘小峰) and Wang Yue(王越) Fine-grained permutation entropy as a measure of natural complexity for time series 2009 Chin. Phys. B 18 2690
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