Modeling user and topic interactions in social networks using Hawkes processes

We present in this paper a framework to model information diffusion in social networks based on linear multivariate Hawkes processes. Our model exploits the effective broadcasting times of information by users, which guarantees a more realistic view of the information diffusion process. The proposed model takes into consideration not only interactions between users but also interactions between topics, which provides a deeper analysis of influences in social networks. We provide an estimation algorithm based on nonnegative matrix factorization techniques, which together with a dimensionality reduction argument is able to discover, in addition, the latent community structure of the social network. We also provide several numerical results of our method.