Anomaly Detection in Time Series of Graphs using Fusion of Graph Invariants

TL;DR

This paper introduces a method for detecting anomalies in time series of graphs by adaptively fusing multiple graph invariants, demonstrating improved accuracy over individual invariants and naive equal weighting through simulations and real data analysis.

Contribution

It proposes an adaptive fusion approach for combining graph invariants, enhancing anomaly detection in time series of graphs beyond existing methods.

Findings

Adaptive fusion outperforms equal weighting in anomaly detection.

Simulation studies validate the effectiveness of the fusion approach.

Real data analysis confirms practical utility of the method.

Abstract

Given a time series of graphs G(t) = (V, E(t)), t = 1, 2, ..., where the fixed vertex set V represents "actors" and an edge between vertex u and vertex v at time t (uv \in E(t)) represents the existence of a communications event between actors u and v during the tth time period, we wish to detect anomalies and/or change points. We consider a collection of graph features, or invariants, and demonstrate that adaptive fusion provides superior inferential efficacy compared to naive equal weighting for a certain class of anomaly detection problems. Simulation results using a latent process model for time series of graphs, as well as illustrative experimental results for a time series of graphs derived from the Enron email data, show that a fusion statistic can provide superior inference compared to individual invariants alone. These results also demonstrate that an adaptive weighting scheme for fusion of invariants performs better than naive equal weighting.