Dirichlet-hawkes processes with applications to clustering continuous-time document streams

Clusters in document streams, such as online news articles, can be induced by their textual contents, as well as by the temporal dynamics of their arriving patterns. Can we lever-age both sources of information to obtain a better clustering of the documents, and distill information that is not possi-ble to extract using contents only? In this paper, we pro-pose a novel random process, referred to as the Dirichlet-Hawkes process, to take into account both information in a unified framework. A distinctive feature of the proposed model is that the preferential attachment of items to clusters according to cluster sizes, present in Dirichlet processes, is now driven according to the intensities of cluster-wise self-exciting temporal point processes, the Hawkes processes. This new model establishes a previously unexplored connec-tion between Bayesian Nonparametrics and temporal Point Processes, which makes the number of clusters grow to ac-commodate the increasing complexity of online streaming contents, while at the same time adapts to the ever chang-ing dynamics of the respective continuous arrival time. We conducted large-scale experiments on both synthetic and real world news articles, and show that Dirichlet-Hawkes processes can recover both meaningful topics and temporal dynamics, which leads to better predictive performance in terms of content perplexity and arrival time of future docu-ments