Complex Network Construction of Multivariate Time Series Using Information Geometry

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.