This paper introduces a refined graph encoder embedding method, enhancing the original graph encoder embedding using 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 via stochastic block models, and 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 a collection of simulated and real-world graph data.

翻译：本文提出了一种精炼的图编码器嵌入方法，通过线性变换、自训练以及观测社区内的隐藏社区恢复机制，增强原始图编码器嵌入的性能。我们为这一精炼过程提供了理论依据，阐释了所提方法如何及为何能通过随机块模型有效识别有用的隐藏社区，并论证了精炼方法如何优化顶点嵌入效果及改善后续顶点分类的决策边界。通过一系列模拟图数据与真实图数据的实验，验证了该方法的有效性。