Graph Adversarial Diffusion Convolution

TL;DR

This paper proposes a novel Graph Adversarial Diffusion Convolution (GADC) model that enhances robustness against adversarial attacks and noise in graph data through a min-max optimization framework, improving performance on heterophilic graphs.

Contribution

It introduces GADC, a new variant of GDC derived from a min-max optimization formulation that incorporates adversarial robustness into graph convolution.

Findings

GADC outperforms GDC on various datasets.

GADC enhances robustness against adversarial attacks.

GADC improves performance on heterophilic graphs.

Abstract

This paper introduces a min-max optimization formulation for the Graph Signal Denoising (GSD) problem. In this formulation, we first maximize the second term of GSD by introducing perturbations to the graph structure based on Laplacian distance and then minimize the overall loss of the GSD. By solving the min-max optimization problem, we derive a new variant of the Graph Diffusion Convolution (GDC) architecture, called Graph Adversarial Diffusion Convolution (GADC). GADC differs from GDC by incorporating an additional term that enhances robustness against adversarial attacks on the graph structure and noise in node features. Moreover, GADC improves the performance of GDC on heterophilic graphs. Extensive experiments demonstrate the effectiveness of GADC across various datasets. Code is available at https://github.com/SongtaoLiu0823/GADC.