Statistical Clustering Analysis Of Recurrent Interactions With Network Snapshots

Complex network analysis has become a major research field at present,and its application has covered all industries,from sociology to ecology,from biology to Internet and so on.Certain results has achieved for such research work and it has been gradually paid attention to and applied in various industries.Most research on networks is based on a static graph,either from an aggregation of data at all times or as a snapshot of data at a particular time.However,such research methods often ignore an important feature of clustering in networked data--the change of clustering population of nodes over time and the evolution of clustering.Therefore,aiming at the above problems,this paper mainly completed the following innovative research contents on cluster analysis:A kind of dynamic network stochastic block model(DSBM)based on recurrent events with network snapshots is expanded based on the Dynamic Stochastic Block Model proposed by Yang et al.(2011)and Matias and Miele(2017).Among them,the model introduced markov transition probability matrix to describe the changing state of cluster community structure in the network on each observation time.For the study of the cumulative number of repeated events,this paper proposes a multiplier intensity function model: a semi-parametric proportional rate model with covariate information.For parameter estimation in this model,it is divided into recurrent part and other part of network parameter estimation.However,the parameters of the two parts are related.Therefore,maximum likelihood is not the best option.First,in the recurrence model,the conditional likelihood function of cumulative number of event observations is established and Parameters were estimated using a consistent algorithm and an estimated equation.And the other parameters were obtained by the Variational Expectation Maximization Algorithm(VEM).Then the iterative formulas of model parameters are derived in detail.In real life,the observed objects in the social network will contain a lot of covariate information,and these observed objects will affect the link between them because of these objects.For example,in the face-to-face social network data of French high school students,students' chosen courses,gender and so on.Since the model in this paper cannot deal with the change of the number of cluster communities,it is assumed in this paper that the number of cluster communities remains unchanged.Two methods:Bayesian Information Criterion(BIC)and likelihood function method are introduced in this paper to determine the number of cluster communities.In order to simplify the processing,the likelihood function method is adopted in this chapter to determine the optimal number of clustering communities under the maximum logarithmic likelihood function value.Then the model proposed in this paper is simulated numerically to evaluate the performance of this model.This model is mainly used to evaluate the partition effect of clustering communities in generating networks under different sample sizes and different time snapshots.In this paper,the Adjusted Rand Index(ARI)under each time snapshot and the global ARI under different sample size and different time snapshot were respectively calculated in numerical simulation to evaluate the partition effect of the model method in this paper on cluster communities.The results show that the larger the number of time snapshots,the larger the sample size,the better the estimation effect of the intensity function in the model,and the more accurate the effect of clustering community partition.Finally,this paper uses the dynamic network Stochastic block model based on recurrent events to do node clustering for the face-to-face social network data of French high school students,carries out empirical analysis,and displays the result of clustering community partition through visual method.The empirical results show that this model demonstrates the partition effect of the model by constructing node membership.