In this work, we study the event occurrences of user activities on online social network platforms. To characterize the social activity interactions among network users, we propose a network group Hawkes (NGH) process model. Particularly, the observed network structure information is employed to model the users dynamic posting behaviors. Furthermore, the users are clustered into latent groups according to their dynamic behavior patterns. To estimate the model, a constraint maximum likelihood approach is proposed. Theoretically, we establish the consistency and asymptotic normality of the estimators. In addition, we show that the group memberships can be identified consistently. To conduct estimation, a branching representation structure is firstly introduced, and a stochastic EM (StEM) algorithm is developed to tackle the computational problem. Lastly, we apply the proposed method to a social network data collected from Sina Weibo, and identify the infuential network users as an interesting application.
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