Graph-structured data is integral to many applications, prompting the development of various graph representation methods. Graph autoencoders (GAEs), in particular, reconstruct graph structures from node embeddings. Current GAE models primarily utilize self-correlation to represent graph structures and focus on node-level tasks, often overlooking multi-graph scenarios. Our theoretical analysis indicates that self-correlation generally falls short in accurately representing specific graph features such as islands, symmetrical structures, and directional edges, particularly in smaller or multiple graph contexts. To address these limitations, we introduce a cross-correlation mechanism that significantly enhances the GAE representational capabilities. Additionally, we propose GraphCroc, a new GAE that supports flexible encoder architectures tailored for various downstream tasks and ensures robust structural reconstruction, through a mirrored encoding-decoding process. This model also tackles the challenge of representation bias during optimization by implementing a loss-balancing strategy. Both theoretical analysis and numerical evaluations demonstrate that our methodology significantly outperforms existing self-correlation-based GAEs in graph structure reconstruction.

翻译：图结构数据在许多应用中不可或缺，这推动了各种图表示方法的发展。图自编码器（GAEs）尤其能够从节点嵌入中重建图结构。当前的GAE模型主要利用自相关来表示图结构，并专注于节点级任务，往往忽视了多图场景。我们的理论分析表明，自相关通常难以准确表示特定的图特征，例如孤立子图、对称结构和有向边，尤其是在较小或涉及多个图的上下文中。为了解决这些局限性，我们引入了一种互相关机制，显著增强了GAE的表征能力。此外，我们提出了GraphCroc，这是一种新的GAE，它通过镜像编码-解码过程，支持为各种下游任务定制的灵活编码器架构，并确保稳健的结构重建。该模型还通过实施损失平衡策略，解决了优化过程中表征偏差的挑战。理论分析和数值评估均表明，我们的方法在图结构重建方面显著优于现有的基于自相关的GAE。