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Chin. Phys. B, 2009, Vol. 18(7): 2690-2695    DOI: 10.1088/1674-1056/18/7/011
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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.
Keywords:  complexity      entropy      dynamical change      fine-grained symbolization  
Received:  10 November 2008      Revised:  11 January 2009      Accepted manuscript online: 
PACS:  05.45.Tp (Time series analysis)  
  02.50.Ey (Stochastic processes)  
  05.70.Ce (Thermodynamic functions and equations of state)  
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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