A Piece-wise Polynomial Filtering Approach for Graph Neural Networks

TL;DR

This paper introduces a novel piece-wise polynomial filtering method for GNNs that adaptively learns spectral filters, significantly improving node classification accuracy especially on heterophilic graphs.

Contribution

The paper proposes an eigendecomposition-based adaptive polynomial filtering approach that enhances GNN performance by learning multiple spectral filters, addressing limitations of existing polynomial models.

Findings

Achieves up to 5% accuracy improvement over state-of-the-art methods.

Effectively learns high-order polynomials through spectral decomposition.

Scalable to large graphs with improved classification results.

Abstract

Graph Neural Networks (GNNs) exploit signals from node features and the input graph topology to improve node classification task performance. However, these models tend to perform poorly on heterophilic graphs, where connected nodes have different labels. Recently proposed GNNs work across graphs having varying levels of homophily. Among these, models relying on polynomial graph filters have shown promise. We observe that solutions to these polynomial graph filter models are also solutions to an overdetermined system of equations. It suggests that in some instances, the model needs to learn a reasonably high order polynomial. On investigation, we find the proposed models ineffective at learning such polynomials due to their designs. To mitigate this issue, we perform an eigendecomposition of the graph and propose to learn multiple adaptive polynomial filters acting on different subsets of the spectrum. We theoretically and empirically show that our proposed model learns a better filter, thereby improving classification accuracy. We study various aspects of our proposed model including, dependency on the number of eigencomponents utilized, latent polynomial filters learned, and performance of the individual polynomials on the node classification task. We further show that our model is scalable by evaluating over large graphs. Our model achieves performance gains of up to 5% over the state-of-the-art models and outperforms existing polynomial filter-based approaches in general.