通过分段常数滤波提升图神经网络对谱特征的捕捉能力
Piecewise Constant Spectral Graph Neural Network
- 采用分段常数与多项式滤波结合，自适应划分频谱区间
- 在9个基准数据集上表现优于传统方法，尤其在异质图上提升显著
- 适合处理复杂谱结构的异质图学习任务，可扩展性强
图神经网络（GNN）在多个领域取得显著成功，得益于其对数据图结构的利用。现有的谱域GNN使用低阶多项式滤波器来捕捉图的谱特性，但因多项式阶数过低，难以充分识别图的谱特征。而提高多项式阶数则计算成本高，且超过一定阈值后性能趋于平缓甚至下降。本文提出分段常数谱图神经网络（PieCoN），将常数谱滤波器与多项式滤波器结合，提供更灵活的图结构利用方式。通过自适应地将频谱划分为多个区间，该方法显著扩展了可有效学习的谱特性范围。在包含同质与异质图在内的9个基准数据集上的实验表明，PieCoN在异质图上表现尤为突出，展现了广泛的应用潜力。
原文摘要 · Abstract (English)
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.
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