Node Feature Kernels Increase Graph Convolutional Network Robustness

TL;DR

This paper demonstrates that incorporating node feature kernels into GCNs enhances their robustness against graph perturbations, supported by theoretical analysis and empirical validation on multiple datasets.

Contribution

It introduces a node feature kernel method for GCNs and provides a theoretical framework explaining its robustness benefits.

Findings

Adding node feature kernels improves GCN robustness to graph perturbations.

Perturbed graphs cause GCN performance to decline, sometimes worse than MLPs on features.

The proposed method significantly enhances GCN performance on real datasets.

Abstract

The robustness of the much-used Graph Convolutional Networks (GCNs) to perturbations of their input is becoming a topic of increasing importance. In this paper, the random GCN is introduced for which a random matrix theory analysis is possible. This analysis suggests that if the graph is sufficiently perturbed, or in the extreme case random, then the GCN fails to benefit from the node features. It is furthermore observed that enhancing the message passing step in GCNs by adding the node feature kernel to the adjacency matrix of the graph structure solves this problem. An empirical study of a GCN utilised for node classification on six real datasets further confirms the theoretical findings and demonstrates that perturbations of the graph structure can result in GCNs performing significantly worse than Multi-Layer Perceptrons run on the node features alone. In practice, adding a node feature kernel to the message passing of perturbed graphs results in a significant improvement of the GCN's performance, thereby rendering it more robust to graph perturbations. Our code is publicly available at:https://github.com/ChangminWu/RobustGCN.