Complex Network Construction of Multivariate Time Series Using Information Geometry
Complex Network Construction of Multivariate Time Series Using Information Geometry
复制标题
利用信息几何构建多元时间序列的复杂网络
DOI：
10.1109/tsmc.2017.2751504
复制
发表时间：
2019-01-01
影响因子：
8.7
通讯作者：
Luo, Jianguo
中科院分区：
文献类型：
--
作者：
Sun, Jiancheng;Yang, Yong;Luo, Jianguo
网络物理系统（CPS）是计算和物理组件之间的紧密耦合集成和交互。在许多情况下，CPS中的信息收集是通过一组分布式传感器提供的，并且所有这些传感器都随时间不断变化。因此，传感器信息通常是时间序列的形式。时间序列分析中一个特别有趣的应用是使用复杂网络来表示和研究系统的行为。复杂网络在分析复杂系统中发挥着重要作用，因为它有助于理解具有不同相互作用单元的系统的拓扑结构。本文基于信息几何理论，提出了一种从多变量时间序列（MTS）中构造复杂网络的可靠方法，该方法允许通过分析关联的复杂网络来提取时间序列中的信息。我们首先估计协方差矩阵，然后引入基于测地线的协方差矩阵之间的距离。因此，网络可以构建在黎曼流形上，其中节点和边分别对应于协方差矩阵和基于测地线的距离。该方法为我们提供了一个非线性关系和内在的几何观点来理解MTS，也是一种替代方法来融合，建模，表示和可视化CPS中的多传感器数据。一些实验研究和数值例子来证明我们的方法与合成和真实的数据集的通用性和有效性。
Cyber physical systems (CPS) is a tightly coupled integration and interaction between computational and physical components. In many cases, information collection in CPS is provided through a group of distributed sensors and all of them change continuously with time. Thus the sensor information is usually in the form of time series. One particularly interesting application in time series analysis is use of complex networks to represent and study behaviors of system. Complex networks has been playing an important role for analyzing complex systems as it helps understanding the topology structure of systems with different interacting units. In this paper, we proposed a reliable method for constructing complex networks from multivariate time series (MTSs) in the cases of single and multisensor based on information geometry theory, which allows the information in the time series to be extracted by analyzing the associated complex network. We first estimate covariance matrices and then a geodesic-based distance between the covariance matrices is introduced. Consequently, the network can be constructed on a Riemannian manifold where the nodes and edges correspond to the covariance matrix and the geodesic-based distance, respectively. The proposed method provides us with a nonlinear relationship and intrinsic geometry viewpoint to understand the MTSs and also an alternative approach to fuse, model, represent, and visualize the multisensor data in CPS. A number of experimental studies and numerical examples are presented to demonstrate the generality and the effectiveness of our approach with both synthetic and real datasets.