The Network Community Detection Method Based On Belief Propagation Algorithm And Dependent Covariates

Network can be seen everywhere in our life, and it can be used to describe many systems , such as social networks, biological networks, communication networks and so on. With the rapid development of network information technology represented by the Internet, people's life and production activities are increasingly dependent on various net-works. We are in urgent need of in-depth excavation of the network, in-depth analysis of network data to solve the problem of the reality network. Nowadays the network com-munity detection is an important research topic, and the network community detection method of the network is in similar nodes into a set ,called the community, making the commnity links between the nodes is more dense, and the connection between the nodes of a community is extremely sparse, we try to find the community classification in the network through the connection and all kinds of node information. The success of network community detection will make the network more clear and more rich explanation, at the same time the community detection will bring to the subsequent development of the value of many reality networks, such as precision marketing and so on.In this paper, we add the covariate information in the traditional stochastic block model, that is to say, we can find the community by the network and covariate of the nodes,which is more in line with reality and the actual needs.In this paper, we prove the feasibility of belief propagation in community detection by proving the equivalence between two methods found in the stochastic block model. And this is why we propose a belief propagation algorithm to estimate the parameters of the network community detection model which covariates in the large and sparse network environment. Due to the fact that the belief propagation algorithm is not reasonable in the network structure with ring, and can not be implemented accurately, it is rarely used in the field of network community detection.However, for large sparse network, we are more concerned about the model accuracy based on low complexity and simple operation ,and through the experimental results we can see that the belief propagation algorithm is more rapid than the traditional EM algorithm and spectral method, and the result is also very accurate.