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. Importantly, this approach requires knowledge of 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 linear combination of the vertices in the training set and uses the recovered coefficients to classify the test vertex. We demonstrate that the sparse representation classifier can predict vertex labels with higher accuracy than adjacency spectral embedding approaches via both a simulation study and real data experiments considering the Caenorhabditis elegans neuronal network and the Enron communication network. Our results demonstrate the robustness of our proposed vertex classifier when the model dimension is unknown.
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