  Dynamic and temporal graphs are rich data structures that are used to model
complex relationships between entities over time. In particular, anomaly
detection in temporal graphs is crucial for many real world applications such
as intrusion identification in network systems, detection of ecosystem
disturbances and detection of epidemic outbreaks. In this paper, we focus on
change point detection in dynamic graphs and address two main challenges
associated with this problem: I) how to compare graph snapshots across time,
II) how to capture temporal dependencies. To solve the above challenges, we
propose Laplacian Anomaly Detection (LAD) which uses the spectrum of the
Laplacian matrix of the graph structure at each snapshot to obtain low
dimensional embeddings. LAD explicitly models short term and long term
dependencies by applying two sliding windows. In synthetic experiments, LAD
outperforms the state-of-the-art method. We also evaluate our method on three
real dynamic networks: UCI message network, US senate co-sponsorship network
and Canadian bill voting network. In all three datasets, we demonstrate that
our method can more effectively identify anomalous time points according to
significant real world events.

Machine Learning;Social and Information Networks;Machine Learning