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

Youngser Park,C. Priebe,Abdou Youssef

Published 2012 in IEEE Journal on Selected Topics in Signal Processing

ABSTRACT

Given a time series of graphs <i>G</i>(<i>t</i>)=(<i>V</i>,<i>E</i>(<i>t</i>)) , <i>t</i>=1,2,... , where the fixed vertex set <i>V</i> represents “actors” and an edge between vertex <i>u</i> and vertex <i>v</i> at time <i>t</i>(<i>uv</i> ∈ <i>E</i>(<i>t</i>)) represents the existence of a communications event between actors <i>u</i> and <i>v</i> during the <i>t</i><sup>th</sup> 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.

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