Locality statistics for anomaly detection in time series of graphs

TL;DR

This paper develops a statistical framework for detecting change-points in dynamic networks modeled by stochastic block models, analyzing the properties of locality-based scan statistics.

Contribution

It derives the limiting distributions and power characteristics of two locality-based scan statistics for change-point detection in time series of graphs.

Findings

Both statistics are admissible in one setting.

One statistic is inadmissible in another setting.

Performance comparison on synthetic and real data.

Abstract

The ability to detect change-points in a dynamic network or a time series of graphs is an increasingly important task in many applications of the emerging discipline of graph signal processing. This paper formulates change-point detection as a hypothesis testing problem in terms of a generative latent position model, focusing on the special case of the Stochastic Block Model time series. We analyze two classes of scan statistics, based on distinct underlying locality statistics presented in the literature. Our main contribution is the derivation of the limiting distributions and power characteristics of the competing scan statistics. Performance is compared theoretically, on synthetic data, and on the Enron email corpus. We demonstrate that both statistics are admissible in one simple setting, while one of the statistics is inadmissible a second setting.