Modeling Temporal Activity Patterns in Dynamic Social Networks

The focus of this work is on developing probabilistic models for user activity in social networks by incorporating the social network influence as perceived by the user. For this, we propose a coupled Hidden Markov Model, where each user's activity evolves according to a Markov chain with a hidden state that is influenced by the collective activity of the friends of the user. We develop generalized Baum-Welch and Viterbi algorithms for model parameter learning and state estimation for the proposed framework. We then validate the proposed model using a significant corpus of user activity on Twitter. Our numerical studies show that with sufficient observations to ensure accurate model learning, the proposed framework explains the observed data better than either a renewal process-based model or a conventional uncoupled Hidden Markov Model. We also demonstrate the utility of the proposed approach in predicting the time to the next tweet. Finally, clustering in the model parameter space is shown to result in distinct natural clusters of users characterized by the interaction dynamic between a user and his network.