On Robust Clustering of Temporal Point Process

TL;DR

This paper introduces a robust clustering framework for temporal point processes that effectively detects outliers and provides theoretical guarantees, improving clustering accuracy in event stream data applications.

Contribution

It proposes a novel, computationally efficient, model-free distance measure and an EM-type algorithm with Catoni's influence function for robust clustering with theoretical analysis.

Findings

Effective outlier detection in event streams

Theoretical guarantees on convergence and error bounds

Successful application to real-world data

Abstract

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.