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Sensors 2017, 17(4), 787; doi:10.3390/s17040787

Measuring Complexity and Predictability of Time Series with Flexible Multiscale Entropy for Sensor Networks

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1,2,* , 1,2
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3,* and 4,*
1
School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China
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
*
Authors to whom correspondence should be addressed.
Received: 15 November 2016 / Revised: 15 March 2017 / Accepted: 24 March 2017 / Published: 6 April 2017
(This article belongs to the Special Issue Topology Control in Emerging Sensor Networks)
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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. View Full-Text
Keywords: time series; complexity; sample entropy; flexible similarity criterion; flexible multiscale entropy; sensor network organizing; sensor network controlling time series; complexity; sample entropy; flexible similarity criterion; flexible multiscale entropy; sensor network organizing; sensor network controlling
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Zhou, R.; Yang, C.; Wan, J.; Zhang, W.; Guan, B.; Xiong, N. Measuring Complexity and Predictability of Time Series with Flexible Multiscale Entropy for Sensor Networks. Sensors 2017, 17, 787.

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