Curvature Graph Generative Adversarial Networks

TL;DR

This paper introduces CurvGAN, a novel GAN-based method for graph representation that models non-Euclidean graph data in Riemannian space, preserving topological properties and handling heterogeneity more effectively.

Contribution

It is the first to apply GANs in Riemannian geometric space for graph data, improving topological preservation and reducing distortion in representations.

Findings

Outperforms state-of-the-art methods across multiple tasks

Shows superior robustness and generalization

Effectively preserves topological properties

Abstract

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.