Title: A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering,
Abstract: We propose an effective method to solve the event sequence clustering
problems based on a novel Dirichlet mixture model of a special but significant
type of point processes --- Hawkes process. In this model, each event sequence
belonging to a cluster is generated via the same Hawkes process with specific
parameters, and different clusters correspond to different Hawkes processes.
The prior distribution of the Hawkes processes is controlled via a Dirichlet
distribution. We learn the model via a maximum likelihood estimator (MLE) and
propose an effective variational Bayesian inference algorithm. We specifically
analyze the resulting EM-type algorithm in the context of inner-outer
iterations and discuss several inner iteration allocation strategies. The
identifiability of our model, the convergence of our learning method, and its
sample complexity are analyzed in both theoretical and empirical ways, which
demonstrate the superiority of our method to other competitors. The proposed
method learns the number of clusters automatically and is robust to model
misspecification. Experiments on both synthetic and real-world data show that
our method can learn diverse triggering patterns hidden in asynchronous event
sequences and achieve encouraging performance on clustering purity and
consistency.