  The general method of graph coarsening or graph reduction has been a
remarkably useful and ubiquitous tool in scientific computing and it is now
just starting to have a similar impact in machine learning. The goal of this
paper is to take a broad look into coarsening techniques that have been
successfully deployed in scientific computing and see how similar principles
are finding their way in more recent applications related to machine learning.
In scientific computing, coarsening plays a central role in algebraic multigrid
methods as well as the related class of multilevel incomplete LU
factorizations. In machine learning, graph coarsening goes under various names,
e.g., graph downsampling or graph reduction. Its goal in most cases is to
replace some original graph by one which has fewer nodes, but whose structure
and characteristics are similar to those of the original graph. As will be
seen, a common strategy in these methods is to rely on spectral properties to
define the coarse graph.
