Monitoring unweighted networks with communities based on latent logit model

Nowadays it is common to see information exchange among certain nodes in various network systems such as Internet of Things (IoT) and social networks. Once anomalies occur in a network system, the interaction frequency will increase or decrease abruptly. Detecting such changes has attracted much attention in the field of statistical process control (SPC). However, limited number of research incorporate the heterogeneity and community information of nodes simultaneously. The loss of information refrains the control chart from detecting network anomalies in a timely manner. In this regard, we propose a logit model with latent factors of nodes and communities to describe the variation of communications within unweighted networks, where the presence and absence of communication between each pair of nodes is regarded as a Bernoulli variable. Then the proposed model is expressed in a matrix form to enable easy parameter estimation and derivation of monitoring statistic. A new control chart is established based on generalized likelihood ratio test (GLRT). The simulation results and two real examples demonstrate the effectiveness and advantages of proposed control chart in comparison with two alternative methods.