Piecewise Constant Spectral Graph Neural Network

TL;DR

This paper introduces PieCoN, a spectral GNN that adaptively partitions the graph spectrum into intervals, combining constant and polynomial filters to better capture spectral properties, especially in heterophilic graphs.

Contribution

PieCoN is a novel spectral GNN that adaptively partitions the spectrum, enhancing spectral property learning beyond traditional polynomial filters.

Findings

Effective on heterophilic datasets

Outperforms existing spectral GNNs in experiments

Flexible spectral filtering approach

Abstract

Graph Neural Networks (GNNs) have achieved significant success across various domains by leveraging graph structures in data. Existing spectral GNNs, which use low-degree polynomial filters to capture graph spectral properties, may not fully identify the graph's spectral characteristics because of the polynomial's small degree. However, increasing the polynomial degree is computationally expensive and beyond certain thresholds leads to performance plateaus or degradation. In this paper, we introduce the Piecewise Constant Spectral Graph Neural Network(PieCoN) to address these challenges. PieCoN combines constant spectral filters with polynomial filters to provide a more flexible way to leverage the graph structure. By adaptively partitioning the spectrum into intervals, our approach increases the range of spectral properties that can be effectively learned. Experiments on nine benchmark datasets, including both homophilic and heterophilic graphs, demonstrate that PieCoN is particularly effective on heterophilic datasets, highlighting its potential for a wide range of applications.