  Clustering of event stream data is of great importance in many application
scenarios, including but not limited to, e-commerce, electronic health, online
testing, mobile music service, etc. Existing clustering algorithms fail to take
outlier data into consideration and are implemented without theoretical
guarantees. In this paper, we propose a robust temporal point processes
clustering framework which works under mild assumptions and meanwhile addresses
several important issues in the event stream clustering problem.Specifically,
we introduce a computationally efficient model-free distance function to
quantify the dissimilarity between different event streams so that the outliers
can be detected and the good initial clusters could be obtained. We further
consider an expectation-maximization-type algorithm incorporated with a
Catoni's influence function for robust estimation and fine-tuning of clusters.
We also establish the theoretical results including algorithmic convergence,
estimation error bound, outlier detection, etc. Simulation results corroborate
our theoretical findings and real data applications show the effectiveness of
our proposed methodology.
