Community-finding Methods Based On The Gaps Of Interactions For The Dynamic Network Data

In reality,there are many network systems in everywhere,but they are quite complex.Community-finding is a research direction of network research.Detecting community structure from complex network is a research hotspot.By identifying these community structures,researchers have gained a better understanding of the functional characteristics of complex networks.In this way,we can deeply explore the nature of the network.Therefore,the community-finding method has been widely used in many fields.The study of the number of recurrent events and the gap between adjacent recurrent events is usually the goal of longitudinal or epidemiological studies.In order to analyze the gap,predecessors proposed corresponding proportional hazard models,such as the Cox proportional hazard model,Anderson-Gill proportional hazard model,PrentissWilliams-Peterson model and so on.However,it is well known that proportional hazards models may not fit the data well.In order to provide an alternative method,this paper studies the additive hazard model,fits the gap data,and evaluates its fitting effect.Compared with the proportional hazard model,one of the main advantages of additive hazard model is that the parameter estimator obtained is in the form of a dominant closedform solution,which greatly reduces the computational difficulty.In early,most community-finding methods can only be entitled to a non-overlapping network of community,and MMSB not only overlapping communities can be found on to the network,can also be quantitative to get the membership degree of node in each community,therefore get widely attention.However,the standard MMSB is not suitable for dynamic networks,which limits its application scope to some extent.In this paper,by studying the existing network community-finding methods and analyzing their advantages and disadvantages,a semi-parametric extension model of MMSB is proposed to model the gap of recurrent interaction events in continuous time using the additive risk model.In other words,the application of recurrent events to vertical network can better study the community structure and nature of the network.In addition,we demonstrate the fitting effect of regression parameters of recurrent events in the simulation,and judge the accuracy of community division of this model.In the application,the effect of this method is illustrated by analyzing a data set.The innovation contents of this paper are as follows:First,Matias et al.(2018),under the assumption of Poisson's hazard function,conducts parameter estimation of the model by means of a completely non-parametric kernel density method,which is of great computational strength due to its involvement in kernel estimation and width selection.And based on the semi-parametric additive average risk model(don't need a Poisson process hypothesis),and allows the node to the covariate exists,use the method of estimating equations of strength as well as covariate parameter estimates,not only ease the distribution assumption of the model,also avoid nuclear estimate complex width selection,so as to greatly reduce the computing intensity and community found precision of the model.The regression parameters and intensity functions of the recurrent event are estimated by the estimation equation,and the network parameters of this model are estimated by the VEM,and the network is divided into communities according to the mixed membership degree of nodes.Secondly,this paper proposes for the recurrence's gap based on node pairs for community-finding.Compared with community-finding based on the cumulative number of recurrence,the gap between recurrence interactions of node pairs is another new perspective on community-finding.