Title: Joint Embedding of Graphs,
Abstract: Feature extraction and dimension reduction for networks is critical in a wide
variety of domains. Efficiently and accurately learning features for multiple
graphs has important applications in statistical inference on graphs. We
propose a method to jointly embed multiple undirected graphs. Given a set of
graphs, the joint embedding method identifies a linear subspace spanned by rank
one symmetric matrices and projects adjacency matrices of graphs into this
subspace. The projection coefficients can be treated as features of the graphs.
We also propose a random graph model which generalizes classical random graph
model and can be used to model multiple graphs. We show through theory and
numerical experiments that under the model, the joint embedding method produces
estimates of parameters with small errors. Via simulation experiments, we
demonstrate that the joint embedding method produces features which lead to
state of the art performance in classifying graphs. Applying the joint
embedding method to human brain graphs, we find it extract interpretable
features that can be used to predict individual composite creativity index.