Robust Vertex Classification

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.

18 pages, 13 figures

References in corpus (5)

• Finding community structure in networks using the eigenvectors of matrices
• The method of moments and degree distributions for network models
• Network histograms and universality of blockmodel approximation
• Vertex nomination schemes for membership prediction
• A Joint Graph Inference Case Study: the C.elegans Chemical and Electrical Connectomes

Cited by in corpus (5)

• One-Hot Graph Encoder Embedding
• Sparse Representation Classification Beyond L1 Minimization and the Subspace Assumption
• Network Dependence Testing via Diffusion Maps and Distance-Based Correlations
• Sparse Representation Classification via Screening for Graphs
• Maximum a Posteriori Inference of Random Dot Product Graphs via Conic Programming