Representing graph data in a low-dimensional space for subsequent tasks is the purpose of attributed graph embedding. Most existing neural network approaches learn latent representations by minimizing reconstruction errors. Rare work considers the data distribution and the topological structure of latent codes simultaneously, which often results in inferior embeddings in real-world graph data. This paper proposes a novel Deep Manifold (Variational) Graph Auto-Encoder (DMVGAE/DMGAE) method for attributed graph data to improve the stability and quality of learned representations to tackle the crowding problem. The node-to-node geodesic similarity is preserved between the original and latent space under a pre-defined distribution. The proposed method surpasses state-of-the-art baseline algorithms by a significant margin on different downstream tasks across popular datasets, which validates our solutions. We promise to release the code after acceptance.

翻译：将图数据表示为低维空间以用于后续任务是属性图嵌入的目的。现有的大多数神经网络方法通过最小化重构误差来学习潜在表示。很少有工作同时考虑数据分布和潜在编码的拓扑结构，这通常会导致在现实图数据中嵌入结果较差。本文提出了一种新颖的深度流形（变分）图自编码器（DMVGAE/DMGAE）方法用于属性图数据，通过改善所学表示的质量与稳定性以解决拥挤问题。在预定义的分布下，原始空间与潜在空间之间的节点间测地相似性得以保持。所提方法在多个流行数据集的不同下游任务上显著超越了最先进的基线算法，验证了我们的解决方案。我们承诺在论文被接收后公开代码。