  For random graphs distributed according to stochastic blockmodels, a special
case of latent position graphs, adjacency spectral embedding followed by
appropriate vertex classification is asymptotically Bayes optimal; but this
approach requires knowledge of and critically depends on the model dimension.
In this paper, we propose a sparse representation vertex classifier which does
not require information about the model dimension. This classifier represents a
test vertex as a sparse combination of the vertices in the training set and
uses the recovered coefficients to classify the test vertex. We prove
consistency of our proposed classifier for stochastic blockmodels, and
demonstrate that the sparse representation classifier can predict vertex labels
with higher accuracy than adjacency spectral embedding approaches via both
simulation studies and real data experiments. Our results demonstrate the
robustness and effectiveness of our proposed vertex classifier when the model
dimension is unknown.
