Synergistic Graph Fusion via Encoder Embedding

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.