  Anomaly detection in massive networks has numerous theoretical and
computational challenges, especially as the behavior to be detected becomes
small in comparison to the larger network. This presentation focuses on recent
results in three key technical areas, specifically geared toward spectral
methods for detection. We first discuss recent models for network behavior, and
how their structure can be exploited for efficient computation of the principal
eigenspace of the graph. In addition to the stochasticity of background
activity, a graph of interest may be observed through a noisy or imperfect
mechanism, which may hinder the detection process. A few simple noise models
are discussed, and we demonstrate the ability to fuse multiple corrupted
observations and recover detection performance. Finally, we discuss the
challenges in scaling the spectral algorithms to large-scale high-performance
computing systems, and present preliminary recommendations to achieve good
performance with current parallel eigensolvers.
