Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of its adjacency or Laplacian matrix, and has found applications throughout the sciences.
We examine two related, complementary inference tasks: the detection of anomalous graphs within a time series, and the detection of temporally anomalous vertices.
In network inference applications, it is often desirable to detect community structure, namely to cluster vertices into groups, or blocks, according to some measure of similarity.
In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure.
Clustering is concerned with coherently grouping observations without any explicit concept of true groupings.
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph.