Discriminant Analysis And Factor Model Of Network Data

With the rapid development of Information technology,The era of complex network is gradually coming.Subsequently,large amount of network data has emerged in modern lives.The analysis of this kind of data is a big challenge for researchers nowadays.In statistics,the analysis of network data has been conducted around two major issues,that is to explore the mode of information spread in the network and reveal the generation mechanism of network structure.This paper also focuses on these two issues.Firstly,on the first issue,we built a statistical model for classification using network structure,called network linear discriminant analysis(NLDA).NLDA model considers both covariate information and network information.For a node with unknown class label,two parts of information can be used for classification.Theoretically,the misclassification rate is studied and an upper bound is derived under mild conditions.Furthermore,it is observed that real networks are often sparse in structure.As a result,asymptotic performance of NLDA is also obtained under certain sparsity assumptions.In order to evaluate the finite sample performance of the newly proposed methodology,a number of simulation studies are conducted,and a real data analysis about Sina Weibo is also presented for illustration purpose.Secondly,on the second issue,high-dimensional factor analysis model is applied to continuous network data and a generative model is constructed.This model assumes that the generation of network is affected by the potential factor structure.It mainly includes potential node sender and receiver effects and higher order dependencies between nodes.Theoretically,under certain assumptions,we obtain the identification conditions of parameters in the model.Furthermore,the consistency and asymptotic normality of the maximum likelihood estimators are proved.In addition,a series of simulation studies are implemented to evaluate the performance of the newly proposed model.