Monitoring networks with overlapping communities based on latent mixed-membership stochastic block model

Currently, objects and people can communicate to formulate various networks such as computer networks, social networks, and protein networks. Anomalies may cause abrupt increases or decreases in the frequency of communications within networks. Many researchers have developed change detection methods to monitor interaction levels based on statistical process control (SPC), a prevalent tool in quality control. However, existing SPC techniques have seldom incorporated the overlapping communities of networks and have shown limited efficiency in detecting shifts at the community level. In addition, it is not convenient to utilize traditional mixed membership stochastic block model (MSBM) for network monitoring due to the complicated parameter estimation. To bridge this research gap, we propose a latent MSBM, which can be expressed in matrix form to enable easy parameter estimation with maximum likelihood estimation (MLE). This model also benefits two monitoring statistics derived from the generalized likelihood ratio test (GLRT). The two finalized change detection methods show higher efficiency than competing approaches in nearly all cases of simulation studies and a real application.