  Change detection in dynamic networks is an important problem in many areas,
such as fraud detection, cyber intrusion detection and health care monitoring.
It is a challenging problem because it involves a time sequence of graphs, each
of which is usually very large and sparse with heterogeneous vertex degrees,
resulting in a complex, high dimensional mathematical object. Spectral
embedding methods provide an effective way to transform a graph to a lower
dimensional latent Euclidean space that preserves the underlying structure of
the network. Although change detection methods that use spectral embedding are
available, they do not address sparsity and degree heterogeneity that usually
occur in noisy real-world graphs and a majority of these methods focus on
changes in the behaviour of the overall network.
  In this paper, we adapt previously developed techniques in spectral graph
theory and propose a novel concept of applying Procrustes techniques to
embedded points for vertices in a graph to detect changes in entity behaviour.
Our spectral embedding approach not only addresses sparsity and degree
heterogeneity issues, but also obtains an estimate of the appropriate embedding
dimension. We call this method CDP (change detection using Procrustes
analysis). We demonstrate the performance of CDP through extensive simulation
experiments and a real-world application. CDP successfully detects various
types of vertex-based changes including (i) changes in vertex degree, (ii)
changes in community membership of vertices, and (iii) unusual increase or
decrease in edge weight between vertices. The change detection performance of
CDP is compared with two other baseline methods that employ alternative
spectral embedding approaches. In both cases, CDP generally shows superior
performance.
