  Graph signal processing (GSP) provides a powerful framework for analyzing
signals arising in a variety of domains. In many applications of GSP, multiple
network structures are available, each of which captures different aspects of
the same underlying phenomenon. To integrate these different data sources,
graph alignment techniques attempt to find the best correspondence between
vertices of two graphs. We consider a generalization of this problem, where
there is no natural one-to-one mapping between vertices, but where there is
correspondence between the community structures of each graph. Because we seek
to learn structure at this higher community level, we refer to this problem as
"coarse" graph alignment. To this end, we propose a novel regularized partial
least squares method which both incorporates the observed graph structures and
imposes sparsity in order to reflect the underlying block community structure.
We provide efficient algorithms for our method and demonstrate its
effectiveness in simulations.
