In this paper, we introduce a novel approach to multi-graph embedding called graph fusion encoder embedding. The method is designed to work with multiple graphs that share a common vertex set. Under the supervised learning setting, we show that the resulting embedding exhibits a surprising yet highly desirable "synergistic effect": for sufficiently large vertex size, the vertex classification accuracy always benefits from additional graphs. We provide a mathematical proof of this effect under the stochastic block model, and identify the necessary and sufficient condition for asymptotically perfect classification. The simulations and real data experiments confirm the superiority of the proposed method, which consistently outperforms recent benchmark methods in classification.

翻译：本文提出了一种名为图融合编码器嵌入的新型多图嵌入方法。该方法专为共享公共顶点集的多个图而设计。在有监督学习场景下，我们证明所得嵌入展现出令人惊讶且极为理想的"协同效应"：当顶点规模足够大时，顶点分类精度总能从额外添加的图中获益。我们在随机分块模型下给出了该效应的数学证明，并确定了实现渐近完美分类的充分必要条件。仿真实验与真实数据实验均验证了所提方法的优越性，其在分类任务中始终优于现有基准方法。