Article Measuring Complexity and Predictability of Time Series with Flexible Multiscale Entropy for Sensor Networks Renjie Zhou 1,2, Chen Yang 1,2, Jian Wan 1,2,*, Wei Zhang 1,2, Bo Guan 3,*, Naixue Xiong 4,* 1 School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China;
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[email protected] (W.Z.) 2 Key Laboratory of Complex Systems Modeling and Simulation of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China 3 School of Electronic and Information Engineer, Ningbo University of Technology, Ningbo 315211, China 4 Department of Mathematics and Computer Science, Northeastern State University, Tahlequah, OK 74464, USA * Correspondence:
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[email protected] (N.X.) Tel.: +1-404-645-4067 (N.X.) Academic Editor: Mohamed F. Younis Received: 15 November 2016; Accepted: 24 March 2017; Published: 6 April 2017 Abstract: Measurement of time series complexity and predictability is sometimes the cornerstone for proposing solutions to topology and congestion control problems in sensor networks. As a method of measuring time series complexity and predictability, multiscale entropy (MSE) has been widely applied in many fields. However, sample entropy, which is the fundamental component of MSE, measures the similarity of two subsequences of a time series with either zero or one, but without in-between values, which causes sudden changes of entropy values even if the time series embraces small changes. This problem becomes especially severe when the length of time series is getting short. For solving such the problem, we propose flexible multiscale entropy (FMSE), which introduces a novel similarity function measuring the similarity of two subsequences with full-range values from zero to one, and thus increases the reliability and stability of measuring time series complexity.