Non-parametric Bayesian Model Of Weighted Complex Network

Recently,more and more researchers in medical and statistical sciences have become interested in functional brain network.With the rise of big data and machine learning in society and the scientific community,The various statistical ideas and statistical models used are also well known to ma^ny people.So those who has been concerned about the mathematical topology of functional brain network,also began to try to use statistical random models.The most famous models are stochastic block models and latent network models and ERGM.Infinite Relation Model(IRM)is a stochastic block model.Resting-state fMRI data constructs a functional brain network by Pearson correlative value and threshold on the time series between any two nodes,the network is unweighted,which can be modeled by IRM,as Andersen did.However,constructing functional brain network by the threshold and getting unweighted network makes the information in original data loss more.this article changes the way Andersen did,retaining positive Pearson correlative values that exceed the threshold as weights in network.And,a new model based on IRM called generalized Infinite Relation Model is proposed in this paper,and applied to functional brain network with weights.In this paper,data simulation and practice of real brain data are made.In the data simulation,the generalized IRM model obtain the correct hidden class of nodes more than 95%.IRM get less correct hidden class of nodes and its result is unstable.In the results of real functional brain network data,using criteria including likelihood values,degree of mean or variance,cluster coefficient,length of characteristic path in sample network obtained by MCMC,connection prediction for two models by ROC and AUC values,to compare two models.All showed that the generalized IRM is much better than IRM.