  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.
