Directed weighted complex networks based on time series symbolic pattern representation
Authors: Zeng Ming  , Wang Er-Hong  , Zhao Ming-Yuan  , Meng Qing-Hao  ,   Tianjin Key Laboratory of Process Measurement and Control, Institute of Robotics and Autonomous Systems, School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
Published: December 2020

Complex networks are capable of modeling different kinds of complex systems in nature and technology, which contain a large number of components interacting with each other in a complicated manner. Quite recently, various approaches to analyzing time series by means of complex networks have been proposed, and their great potentials for uncovering valuable information embedded in time series, especially when nonlinear dynamical systems are incapable of being described by theoretical models have been proven. Despite the existing contributions, up to now, mapping time series into complex networks is still a challenging problem. In order to more effectively dig out the structural characteristics of time series (especially the nonlinear time series) and simplify the computational complexity of time series analysis, in this paper we present a novel method of constructing a directed weighted complex network based on time series symbolic pattern representation combined with sliding window technique. The proposed method firstly implements symbolic procession according to the equal probability segment division and then combines with the sliding window technique to determine the symbolic patterns at different times as nodes of the network. Next, the transition frequency and direction of symbolic patterns are set as the weights and directions of the network edges, thus establishing the directed weighted complex network of the analyzed time series. The results of test using the Logistic system with different parameter settings show that the topological structures of the directed weighted complex network can not only intuitively distinguish the periodic time series and chaotic time series, but also accurately reflect the subtle changes of two types of time series. These results are superior to those from the classical visibility graph method which can be only roughly classified as two types of signals. Finally, the proposed technique is used to investigate the natural wind field signals collected at an outdoor open space in which nine high precision two-dimensional (2D) ultrasonic anemometers are deployed in line with 1 m interval. The topological parameters of the network analysis include the network size, weighted clustering coefficient, and average path length. The corresponding results of our approach indicate that the values of three network parameters show consistent increase or decrease trend with the spatial regular arrangement of the nine anemometers. While the results of the visibility graph network parameters are irregular, and cannot accurately predict the spatial deployment relationship of nine 2D ultrasonic anemometers. These interesting findings suggest that topological features of the directed weighted complex network are potentially valuable characteristics of wind signals, which will have broad applications in researches such as wind power prediction, wind pattern classification and wind field dynamic analysis.