Generative adversarial network (GAN) is widely used for generalized and
robust learning on graph data. However, for non-Euclidean graph data, the
existing GAN-based graph representation methods generate negative samples by
random walk or traverse in discrete space, leading to the information loss of
topological properties (e.g. hierarchy and circularity). Moreover, due to the
topological heterogeneity (i.e., different densities across the graph
structure) of graph data, they suffer from serious topological distortion
problems. In this paper, we proposed a novel Curvature Graph Generative
Adversarial Networks method, named \textbf{\modelname}, which is the first
GAN-based graph representation method in the Riemannian geometric manifold. To
better preserve the topological properties, we approximate the discrete
structure as a continuous Riemannian geometric manifold and generate negative
samples efficiently from the wrapped normal distribution. To deal with the
topological heterogeneity, we leverage the Ricci curvature for local structures
with different topological properties, obtaining to low-distortion
representations. Extensive experiments show that CurvGAN consistently and
significantly outperforms the state-of-the-art methods across multiple tasks
and shows superior robustness and generalization.

本文提出了一种在黎曼几何流形上使用的新型曲率图生成对抗网络方法 Curvature Graph Generative Adversarial Networks，通过利用连续的黎曼几何流形逼近离散数据结构以及从被包裹的正态分布中高效生成负样本，更好地保留了拓扑特性，并借助于具有不同拓扑特性的局部结构的叶齐曲率来应对拓扑异质性问题，实验证明该方法相对于现有最先进的方法在多项任务上表现出了显著的优越性和稳健性。