title: Measuring Complexity and Predictability of Time Series with Flexible Multiscale Entropy for Sensor Networks.
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. The proposed method is evaluated on both synthetic and real time series, including white noise, 1/f noise and real vibration signals. The evaluation results demonstrate that FMSE has a significant improvement in reliability and stability of measuring complexity of time series, especially when the length of time series is short, compared to MSE and composite multiscale entropy (CMSE). The proposed method FMSE is capable of improving the performance of time series analysis based topology and traffic congestion control techniques.
authors.affiliation: School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China. renjie_zhou@163.com.|Key Laboratory of Complex Systems Modeling and Simulation of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China. renjie_zhou@163.com.
authors.forename: Renjie
authors.initials: R
authors.lastname: Zhou
authors.affiliation: School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China. yc320719@live.com.|Key Laboratory of Complex Systems Modeling and Simulation of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China. yc320719@live.com.
authors.forename: Chen
authors.initials: C
authors.lastname: Yang
authors.affiliation: School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China. wanjian@hdu.edu.cn.|Key Laboratory of Complex Systems Modeling and Simulation of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China. wanjian@hdu.edu.cn.
authors.forename: Jian
authors.initials: J
authors.lastname: Wan
authors.affiliation: School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China. magherozhw@hdu.edu.cn.|Key Laboratory of Complex Systems Modeling and Simulation of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China. magherozhw@hdu.edu.cn.
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang
authors.affiliation: School of Electronic and Information Engineer, Ningbo University of Technology, Ningbo 315211, China. guanbo@zjinfo.gov.cn.
authors.forename: Bo
authors.initials: B
authors.lastname: Guan
authors.affiliation: Department of Mathematics and Computer Science, Northeastern State University, Tahlequah, OK 74464, USA. xiongnaixue@gmail.com.
authors.forename: Naixue
authors.initials: N
authors.lastname: Xiong
keywords: complexity; flexible multiscale entropy; flexible similarity criterion; sample entropy; sensor network controlling; sensor network organizing; time series