Community Detection In Networks Based On The Stochastic Block Model

With the rapid development of the Internet industry and the increasing number of network data, it becomes more important to obtain useful information among it. For example, as for the data of mobile phone theme, if we classify the themes according to users' behavior and then make the appropriate recommendation, the user's activity can be greatly enhanced. However, most of the community detection algorithms can not be applied to such data because of it is big data which has sparse network.For each mobile phone theme, Operation Department can be classified into specific category according to its content. Users can choose their favorite type by the category. However, this classification method may not satisfy most of the users. If the theme is classified according to the behavior of all the users, the user's preferences can be satisfied to a large extent. It becomes possible to recommend other relative theme of the same class to users based on their favorite theme. This classification is more likely to be accepted by users.This paper transforms the data of theme from a phone desktop company into network data. In the network graph, each theme is a node. If a user have the same operation for two different themes, then there is a connection between the two themes. In this case, a large sparse matrix is generated. In this paper, the relation between the classes and the distribution of classes are considered parameters. The pseudo likelihood function can be calculated according to adjacency matrix of the network data. Then, the EM algorithm is used to estimate the parameter, and the result of clustering is generated. A iterative method was given to select the number of classes.Finally, the algorithm is applied to the practical data, which is proved that it is indeed related with users'preference.