Clustering Event Streams With Low Rank Hawkes Processes

Abstract

We introduce a fast algorithm for parameter estimation in multidimensional Hawkes processes, a widely used class of temporal point processes for mutually exciting discrete event data. Our approach assumes a low-rank structure on the infectivity parameter of the multidimensional Hawkes process, and relies on a method of moments estimator. Notably, it requires only a single scan of the data, and consistently recovers an accurate representation of the underlying graph structure, while sidestepping numerical stability issues inherent in Hawkes process estimation. Finally, we make connections between our method and spectral clustering, and observe that our contributions result in natural methods for clustering temporal point processes. Our algorithm can be used for community detection and graph cluster discovery in large networks of asynchronous event streams such as high-dimensional neural spike trains, log streams of large computer networks, or high-frequency financial data. We present favorable empirical results on synthetic data, and an application to clustering currency pairs via high-frequency price jumps.