  The unsupervised learning of community structure, in particular the
partitioning vertices into clusters or communities, is a canonical and
well-studied problem in exploratory graph analysis. However, like most graph
analyses the introduction of immense scale presents challenges to traditional
methods. Spectral clustering in distributed memory, for example, requires
hundreds of expensive bulk-synchronous communication rounds to compute an
embedding of vertices to a few eigenvectors of a graph associated matrix.
Furthermore, the whole computation may need to be repeated if the underlying
graph changes some low percentage of edge updates. We present a method inspired
by spectral clustering where we instead use matrix sketches derived from random
dimension-reducing projections. We show that our method produces embeddings
that yield performant clustering results given a fully-dynamic stochastic block
model stream using both the fast Johnson-Lindenstrauss and CountSketch
transforms. We also discuss the effects of stochastic block model parameters
upon the required dimensionality of the subsequent embeddings, and show how
random projections could significantly improve the performance of graph
clustering in distributed memory.
