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.

本研究解决了现有谱图神经网络在识别图谱特性时的局限性，尤其是高阶多项式滤波器的计算复杂性及性能瓶颈。通过引入分段常数滤波器与多项式滤波器结合的分段常数谱图神经网络（PieCoN），该方法能够更灵活地利用图结构并提高谱特性的学习能力。实验结果表明，PieCoN在异构图数据集上表现尤为优秀，展示了其在广泛应用中的潜力。