When Does A Spectral Graph Neural Network Fail in Node Classification?

TL;DR

This paper analyzes when spectral GNNs fail in node classification by examining their prediction errors and introduces a data-driven filter bank strategy to improve performance, supported by theoretical insights and experiments.

Contribution

It provides a theoretical framework linking graph structure and filter response efficiency to GNN failure, proposing a novel filter design strategy.

Findings

Low response efficiency on label differences leads to GNN failure.

Data-driven filter banks improve GNN performance.

Experimental results validate theoretical predictions.

Abstract

Spectral Graph Neural Networks (GNNs) with various graph filters have received extensive affirmation due to their promising performance in graph learning problems. However, it is known that GNNs do not always perform well. Although graph filters provide theoretical foundations for model explanations, it is unclear when a spectral GNN will fail. In this paper, focusing on node classification problems, we conduct a theoretical analysis of spectral GNNs performance by investigating their prediction error. With the aid of graph indicators including homophily degree and response efficiency we proposed, we establish a comprehensive understanding of complex relationships between graph structure, node labels, and graph filters. We indicate that graph filters with low response efficiency on label difference are prone to fail. To enhance GNNs performance, we provide a provably better strategy for filter design from our theoretical analysis - using data-driven filter banks, and propose simple models for empirical validation. Experimental results show consistency with our theoretical results and support our strategy.