Piecewise Constant Spectral Graph Neural Network
This work addresses a bottleneck in spectral GNNs for graph learning tasks, particularly benefiting applications with heterophilic graphs, though it is incremental as it builds on existing spectral methods.
The paper tackled the limitation of spectral GNNs in capturing graph spectral properties by introducing PieCoN, which combines constant and polynomial filters to adaptively partition the spectrum, resulting in improved performance on heterophilic datasets across nine benchmarks.
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.