Reconstruction Of Time-varying Complex Networks Incorporating Structure Priors

The network topology is a particularly important and fundamental element in network science research.However,in some cases,we can only observe some dynamic information of the nodes in the network,rather than the topology itself.How to infer network structure from the dynamic data of the nodes is an important content of network reconstruction.This thesis focuses on the network reconstruction,especially on the time-varying network.By aiming at the dynamic changes of the network structure,and fusing the prior information of the network structure,new reconstruction algorithms are proposed to improve the reconstruction accuracy.The main contents of the thesis include:For piecewise time-varying networks,Kalman filtering is used to estimate the change points of the network at which the structure will alter.And then the time series data can be segmented,based on which the structural priors are incorporated into network inference when designing reconstruction algorithms.In particular,as for uniform networks,two different reconstruction algorithms incorporating average degree are proposed.As for non-uniform networks,an adaptive algorithm incorporating power-law characteristics is given.According to cross simulation verification on different network types,the proposed algorithms can greatly improve the accuracy of network reconstruction.Further,the proposed algorithms are applied to the structural inference of brain functional networks for both normal group and teenager social anxiety disorder group,under rest-state and task-state respectively.Based on the result,it can be found that the brain network structures of abnormal groups are significantly different from the normal ones,which could be contributed to the diagnosis of teenager social anxiety disorder.For continuous time-varying networks,the sliding window is proposed to smooth the data around the current time point by reweighting the contribution of each time point in the optimization process for the network inference at the current moment.Based on smooth algorithm,the prior information of the network structure is further incorporated into reconstruction algorithms.In particular,for uniform networks,an adaptive algorithm combining average strength and latent structure is proposed.Further,a reconstruction algorithm based on the average strength optimization is proposed as well.As for non-uniform networks,a reconstruction algorithm combining sliding window and power-law characteristics is proposed.According to simulation verification on different network types,the proposed algorithms can effectively improve the accuracy of network reconstruction.In addition,nonlinear networked systems with unknown node's dynamics are considered,combining system identification.A network reconstruction method based on basic-functiondictionary selection is proposed to infer network structure.