Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph machine learning, with polynomial filters applied for graph convolutions, where all nodes share the identical filter weights to mine their local contexts. Despite the success, existing spectral GNNs usually fail to deal with complex networks (e.g., WWW) due to such homogeneous spectral filtering setting that ignores the regional heterogeneity as typically seen in real-world networks. To tackle this issue, we propose a novel diverse spectral filtering (DSF) framework, which automatically learns node-specific filter weights to exploit the varying local structure properly. Particularly, the diverse filter weights consist of two components -- A global one shared among all nodes, and a local one that varies along network edges to reflect node difference arising from distinct graph parts -- to balance between local and global information. As such, not only can the global graph characteristics be captured, but also the diverse local patterns can be mined with awareness of different node positions. Interestingly, we formulate a novel optimization problem to assist in learning diverse filters, which also enables us to enhance any spectral GNNs with our DSF framework. We showcase the proposed framework on three state-of-the-arts including GPR-GNN, BernNet, and JacobiConv. Extensive experiments over 10 benchmark datasets demonstrate that our framework can consistently boost model performance by up to 4.92% in node classification tasks, producing diverse filters with enhanced interpretability. Code is available at \url{https://github.com/jingweio/DSF}.

翻译：谱图神经网络在图形机器学习领域取得了巨大成功，其中图卷积采用多项式滤波器，所有节点共享相同的滤波器权重以挖掘局部上下文。尽管取得了成功，现有谱图神经网络通常难以处理复杂网络（如万维网），因为这种同质化谱滤波设置忽略了现实网络中常见的区域异质性。为解决此问题，我们提出了一种新颖的多样化谱滤波框架，该框架自动学习节点特定的滤波器权重以恰当利用变化的局部结构。具体而言，多样化滤波器权重包含两个部分：一个全局共享权重，所有节点共同使用；一个局部权重，沿网络边变化以反映不同图区域导致的节点差异性——以此平衡局部和全局信息。这样，不仅可以捕获全局图特性，还能意识到不同节点位置来挖掘多样化的局部模式。有趣的是，我们提出了一个新的优化问题来辅助学习多样化滤波器，这使我们能够用DSF框架增强任何谱图神经网络。我们在三种最新模型（GPR-GNN、BernNet和JacobiConv）上展示了所提框架。在10个基准数据集上的大量实验表明，我们的框架在节点分类任务中能持续提升模型性能高达4.92%，并生成具有增强可解释性的多样化滤波器。代码发布于\url{https://github.com/jingweio/DSF}。