基于概率穿越可视图的时间序列网络多重分形研究与应用

Research and Application on Multi-fractals of Complex Network for Time Series Based on Probability Penetrable Visibility Graph

对有限穿越可视图进行改进,提出了概率穿越可视图.首先,将间接可视的节点之间的关联处理为穿越距离的函数,而且节点之间的关联随穿越距离的增加而减小,从而将无权图形式的时间序列网络推广到带权图;其次,采用复杂网络中的网络维数计算方法处理所得到的时间序列网络的分形维数,从而对其自相似特性进行分析;最后,通过划分不同的时间粒度得到多个不同的时间序列网络,对应有多个不同的分形维数,进而分析了所得到的时间序列网络的多重分形特性.在与经典的可视图法、水平可视图法及有限穿越可视图法的对比中论证了所提出的概率穿越可视图的优势.

In this paper,the probability penetrable visibility graph is proposed by improving limited penetrable visibility graph.Firstly,by treating the association of indirectly visible node pairs as a function of penetrable distance with the association of node pairs decreasing with the increasing of penetrable distance,the form of complex network for time series extended from unweighted graph to weighted graph.Secondly,the self-similarity characteristics of complex network for time series can be analyzed with the fractal dimension by using network dimension calculation method for complex network on complex network for time series obtained.Finally,various complex networks for time series appending with various fractal dimensions will be obtained by dividing time series with different time granularity,thus the multi-fractal characteristics of complex network for time series obtained can be analyzed.The feasibility and effectiveness of proposed probability penetrable visibility graph is confirmed compared with the classical visibility graph,horizontal visibility graph and limited penetrable visibility graph.