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

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
∈
E
(
t
)) represents the existence of a communications event between actors
u
and
v
during the
t
^th
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.