Robust Vertex Classification
This addresses a robustness issue in graph analysis for researchers and practitioners working with network data where model parameters are uncertain.
The paper tackles the problem of vertex classification in stochastic blockmodel graphs when the model dimension is unknown, proposing a sparse representation classifier that achieves higher accuracy than existing adjacency spectral embedding approaches.
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.