Research On Complex Network Reconstruction Method Based On Time Series

The topological structure of complex networks plays an important role in social,technological,and biological systems,and is one of the basic elements for conducting complex network analysis.However,in many practical situations,the topology of the network is hidden or cannot be directly obtained.Therefore,in the case of unknown network topology,inferring network structure through the time series of observable nodes is the key to analyzing system performance and the foundation for achieving system optimization.The limited noise measurement data of system dynamics,the curse of dimensionality of large-scale networks and the data loss caused by hidden nodes make the reconstruction of complex networks more challenging.Through indepth research on existing complex network reconstruction techniques,the thesis proposes corresponding time series based complex network reconstruction methods for different types of networks.The main contributions are stated as follows:(1)Aiming at the reconstruction of the unweighted network and the detection and location of hidden nodes,a method of unweighted network reconstruction and hidden node detection based on compressed sensing theory is proposed.Firstly,to improve the accuracy of network reconstruction and the processing capacity of large-scale networks,the paper uses the alternating direction method of multipliers to solve the compressed sensing model and introduces regularization technology to increase the numerical stability of the solution.Secondly,when there are hidden nodes in the network,the above reconstruction method is used for hidden node detection and single hidden node localization.Finally,the effectiveness of the method was verified through numerical simulation experiments.(2)Based on hierarchical Bayesian theory,a weighted network reconstruction and hidden node detection method is proposed for the reconstruction of weighted networks and the detection and localization of hidden nodes.Firstly,when there are no hidden nodes in the network,the method can accurately achieve both network structure reconstruction and weight recognition in noisy environments.Secondly,when there are both noise and hidden nodes in the network,to improve the success rate of identifying abnormal nodes and ensure the positioning accuracy of hidden nodes,the above reconstruction method is applied to hidden node detection and single hidden node positioning.Finally,the effectiveness of the method was verified through numerical simulation experiments.(3)A fully data-driven complete network reconstruction method for multi hidden node network topology is proposed based on prisoner evolution game dynamics for the problem of complete network topology reconstruction involving multiple hidden nodes.Firstly,based on the reconstruction methods in work(1)or work(2),reconstruct the partial topology between observable nodes as prior structural information.Then,by analyzing the sequence of payoff differences between nodes and the characteristics of game data,a two-step strategy is proposed to infer the local topology related to hidden nodes,thereby achieving complete network topology reconstruction.At the same time,the method also achieves precise localization and quantity estimation of multiple hidden nodes.Finally,the effectiveness of this method was verified through numerical simulations of several typical networks.