Research On Reconstructing Complex Networks From Time Series

In the real world,complex networks are everywhere,which almost cover all the fields of human life.But in many cases,network topology is invisible and even unknown.How to uncover the network structure from observed data is an important problem for the study of complex networks,which is also the basis of analyzing the performance of the systems.With the facts of the complexity of system dynamics,the limited noisy measurements and the dimensional disaster of the large-scale networks,complex network reconstruction has become even more challenging.Based on the comparison and analysis of existing methods,this dissertation synthetically considers many properties of real networks,including sparsity,nonlinearity,causality,as well as time delayed and time-varying structural characteristics.In view of the insufficiency in many current methods,several kinds of methods are specifically put forward for network reconstruction based on time series.Sparsity and nonlinearity are two main veins throughout the full text,which are also the premise and foundation of all the proposed methods in this dissertation.The main works can be summarized as follows:1.Based on the nonlinearity,sparsity and causality of real networks,a novel method,termed Group Lasso Nonlinear Conditional Granger Causality(GLasso-NCGC),is proposed for reconstructing networks.Rather than identifying parameters of complex systems governed by pre-defined models or taking some functions of model as a prior information,the general framework of nonlinear conditional Granger causality model is first built and then group lasso regression is utilized to select the candidate sets of variables.Finally,nonlinear conditional Granger causality is executed to obtain the causal network.In the simulation of model,the results are assessed with different types of simulated datasets from nonlinear vector autoregressive model,biochemical reaction network model,gene regulatory network model and mutualistic network model.Meanwhile,the performance is also investigated on the number of samples,the effect of noise intensity and the type of network structure,respectively.In the application of benchmark datasets,public datasets from Dream Challenge are used for further verification.Compared with other popular methods,all of the results demonstrate GLasso-NCGC has the best performance and robustness.2.Based on the consideration of time delays in real networks,the problem of network reconstruction with nonuniform lags is further discussed and a novel method is proposed for reconstructing time-delayed networks,termed Nonuniform Embedding Nonlinear Conditional Granger Causality(NENCGC).In detail,nonuniform embedding scheme based on information theory is first adopted to select candidate lagged components and then these selected lagged components are divided into several groups in terms of according different nodes.A series of the lagged components in the same group are treated as a whole through radial basis functions to fit the nonlinear rela-tionships among nodes.In the simulation,the performance is evaluated on several models,such as nonlinear vector autoregressive model and nonlinear time-delayed dynamic models.Particularly,the discrete time-delayed Mackey-Glass model is used for detailed analysis.With the comparison of other popular methods,all of the results demonstrate the superiority of NENCGC.Meanwhile,the robustness of NENCGC against the variations of samples,time-delays,noise intensities,as well as coupling strengths,is demonstrated.In the end,the accurate results are also obtained based on the simulation of the continuous time-delayed gene regulatory model.Moreover,it should be further illustrated that it's important to select lagged components based on the comparison of NENCGC and GLasso-NCGC.GLasso-NCGC can not be fit for inferring time-delayed networks with nonuniform lags.Although NENCGC could be used to network reconstruction without time delays,in this case,GLasso-NCGC is more efficient and has relatively stronger robustness.3.In order to identify the weights of complex networked system,some prior information of the system should be used and a new method based on Bayesian compressive sensing is proposed for reconstructing time-varying weighted networks.Firstly,the space of all possible linear or nonlinear basis functions could be built based on the type of systems and the general framework of nonlinear time-varying network model is established.Then the parameter estimation of nonlinear time-varying network model is turned into the problem of Bayesian compressive sensing and sparse Bayesian learning is adopted to select the corresponding basis functions for time-varying parameters identification.This method not only considers the identification of the structure,but also can track the change of weights.With the introduction of Laplace prior,this method can make the estimated parameters have higher sparsity and accuracy.At the same time,all the unknown parameters could be estimated from observed data without the user-intervention.Finally,both the time-varying biochemical network model and time-varying gene regulatory network model are used to verify the effectiveness of this method.