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 this https URL

本文介绍了一个图信号去噪问题的极小极大优化方法，通过引入以拉普拉斯距离为基础的图结构扰动来最大化图信号去噪中的第二项，并最小化整体损失，从而得到了图扩散卷积的新变种，称为图对抗性扩散卷积。不同于图扩散卷积，图对抗性扩散卷积还融合了一项额外的内容，以增强对图结构上的对抗性攻击和节点特征噪声的鲁棒性。此外，图对抗性扩散卷积在异质图上改进了图扩散卷积的性能。大量实验证明了图对抗性扩散卷积在各种数据集上的有效性。代码可在此网址获得：https:// 此 URL 地址。

图对抗扩散卷积

Graph Adversarial Diffusion Convolution

Graph convolution is the core of most Graph Neural Networks (GNNs) and
usually approximated by message passing between direct (one-hop) neighbors. In
this work, we remove the restriction of using only the direct neighbors by
introducing a powerful, yet spatially localized graph convolution: Graph
diffusion convolution (GDC). GDC leverages generalized graph diffusion,
examples of which are the heat kernel and personalized PageRank. It alleviates
the problem of noisy and often arbitrarily defined edges in real graphs. We
show that GDC is closely related to spectral-based models and thus combines the
strengths of both spatial (message passing) and spectral methods. We
demonstrate that replacing message passing with graph diffusion convolution
consistently leads to significant performance improvements across a wide range
of models on both supervised and unsupervised tasks and a variety of datasets.
Furthermore, GDC is not limited to GNNs but can trivially be combined with any
graph-based model or algorithm (e.g. spectral clustering) without requiring any
changes to the latter or affecting its computational complexity. Our
implementation is available online.

本文提出了一种名为 GDC 的基于图扩散的图卷积方法，与传统的基于直接邻接节点的图卷积方法相比，它可以处理真实图中任意定义边界带来的噪点问题，并在各种图神经网络和其他基于图的算法中取得了显著的性能提升，同时不需要改变原算法的计算复杂度。