Robust Graph Neural Network based on Graph Denoising

TL;DR

This paper introduces a robust GNN framework that explicitly models and mitigates the effects of topological noise and perturbations, improving performance on noisy or adversarial graphs.

Contribution

It proposes an optimization-based robust GNN method that jointly estimates the true graph and learns the GNN parameters, accommodating various types of graph perturbations.

Findings

Enhanced robustness to noisy and adversarial graph perturbations.

Effective joint optimization of graph structure and GNN parameters.

Versatile approach applicable to different graph types.

Abstract

Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to errors stemming from observational noise, graph-learning limitations, or adversarial attacks. If ignored, these perturbations may drastically hinder the performance of GNNs. To address this limitation, this work proposes a robust implementation of GNNs that explicitly accounts for the presence of perturbations in the observed topology. For any task involving GNNs, our core idea is to i) solve an optimization problem not only over the learnable parameters of the GNN but also over the true graph, and ii) augment the fitting cost with a term accounting for discrepancies on the graph. Specifically, we consider a convolutional GNN based on graph filters and follow an alternating optimization approach to handle the (non-differentiable and constrained) optimization problem by combining gradient descent and projected proximal updates. The resulting algorithm is not limited to a particular type of graph and is amenable to incorporating prior information about the perturbations. Finally, we assess the performance of the proposed method through several numerical experiments.