Refined Graph Encoder Embedding via Self-Training and Latent Community Recovery

Abstract: This paper introduces a refined graph encoder embedding method, enhancing the original graph encoder embedding through linear transformation, self-training, and hidden community recovery within observed communities. We provide the theoretical rationale for the refinement procedure, demonstrating how and why our proposed method can effectively identify useful hidden communities under stochastic block models. Furthermore, we show how the refinement method leads to improved vertex embedding and better decision boundaries for subsequent vertex classification. The efficacy of our approach is validated through numerical experiments, which exhibit clear advantages in identifying meaningful latent communities and improved vertex classification across a collection of simulated and real-world graph data.