基于时间序列符号化模式表征的有向加权复杂网络

Directed weighted complex networks based on time series symbolic pattern representation

时间序列复杂网络分析近些年已发展成为非线性信号分析领域的一个国际热点课题.为了能更有效地挖掘时间序列(特别是非线性时间序列)中的结构特征,同时简化时间序列分析的复杂度,提出了一种新的基于时间序列符号化结合滑窗技术模式表征的有向加权复杂网络建网方法.该方法首先按照等概率区段划分的方式将时间序列做符号化处理,结合滑窗技术确定不同时刻的符号化模式作为网络的节点;然后将待分析时间序列符号化模式的转换频次和方向作为网络连边的权重和方向,从而建立时间序列有向加权复杂网络.通过对Logistic系统不同参数设置对应的时间序列复杂网络建网测试结果表明,相比经典的可视图建网方法,本文方法的网络拓扑能更简洁、直观地展示时间序列的结构特征.进而,将本文方法应用于规则排列采集的自然风场信号分析,其网络特性指标能较准确地预测采集信号的排布规律,而可视图建网方法的网络特性指标没有任何规律性的结果.

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（2 D） 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 2 D 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.