Robust Vertex Classification

TL;DR

This paper introduces a robust vertex classification method for stochastic blockmodels that does not require prior knowledge of the model dimension, outperforming spectral embedding approaches in accuracy.

Contribution

A new sparse representation vertex classifier that is consistent and effective without knowing the model dimension in stochastic blockmodels.

Findings

The classifier is consistent for stochastic blockmodels.

It predicts vertex labels more accurately than spectral embedding methods.

Demonstrated effectiveness through simulations and real data.

Abstract

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.