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Entropy 2016, 18(9), 328; doi:10.3390/e18090328

Inferring Weighted Directed Association Networks from Multivariate Time Series with the Small-Shuffle Symbolic Transfer Entropy Spectrum Method

1
Beijing Key Laboratory of Work Safety Intelligent Monitoring, Beijing University of Posts and Telecommunications, Beijing 100876, China
2
School of Information Engineering, Xuchang University, Xuchang 461000, China
*
Author to whom correspondence should be addressed.
Academic Editors: Jinfeng Wang and Kevin H. Knuth
Received: 14 June 2016 / Revised: 12 August 2016 / Accepted: 2 September 2016 / Published: 7 September 2016
(This article belongs to the Special Issue Transfer Entropy II)
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Abstract

Complex network methodology is very useful for complex system exploration. However, the relationships among variables in complex systems are usually not clear. Therefore, inferring association networks among variables from their observed data has been a popular research topic. We propose a method, named small-shuffle symbolic transfer entropy spectrum (SSSTES), for inferring association networks from multivariate time series. The method can solve four problems for inferring association networks, i.e., strong correlation identification, correlation quantification, direction identification and temporal relation identification. The method can be divided into four layers. The first layer is the so-called data layer. Data input and processing are the things to do in this layer. In the second layer, we symbolize the model data, original data and shuffled data, from the previous layer and calculate circularly transfer entropy with different time lags for each pair of time series variables. Thirdly, we compose transfer entropy spectrums for pairwise time series with the previous layer’s output, a list of transfer entropy matrix. We also identify the correlation level between variables in this layer. In the last layer, we build a weighted adjacency matrix, the value of each entry representing the correlation level between pairwise variables, and then get the weighted directed association network. Three sets of numerical simulated data from a linear system, a nonlinear system and a coupled Rossler system are used to show how the proposed approach works. Finally, we apply SSSTES to a real industrial system and get a better result than with two other methods. View Full-Text
Keywords: network inference; multivariate time series; surrogate data method; transfer entropy network inference; multivariate time series; surrogate data method; transfer entropy
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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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Hu, Y.; Zhao, H.; Ai, X. Inferring Weighted Directed Association Networks from Multivariate Time Series with the Small-Shuffle Symbolic Transfer Entropy Spectrum Method. Entropy 2016, 18, 328.

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