提出分块图滤波框架,统一节点与图级滤波,提升异质图性能。
Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening
- 通过图粗化和聚类生成节点分块,分块内进行滤波
- 在基准数据集上优于传统图/节点级滤波方法,异常检测效果显著
- 适合处理兼具同质与异质特性的复杂图结构,兼顾效率与泛化
基于滤波的图神经网络是一类通过图滤波处理图结构数据的方法,在各类图任务中表现优异。传统方法采用全局统一滤波,但在异质图上表现受限。近期工作引入节点级滤波以增强适应性,但存在参数过多、易过拟合风险。本文提出协同粗化的分块滤波(CPF)框架,先通过图粗化算法获得结构感知的节点分块,再用特征空间k-means聚类生成特征感知分块,分别进行分块级滤波。理论分析表明,该框架能有效融合图级与节点级滤波的优势。在多个基准节点分类任务及真实世界图异常检测应用中,CPF均展现出优越性能,验证了其有效性与实用性。
原文摘要 · Abstract (English)
Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise filtering paradigm, imposing a uniform filter across all nodes, yet recent findings suggest that this rigid paradigm struggles with heterophilic graphs. To overcome this, recent works have introduced node-wise filtering, which assigns distinct filters to individual nodes, offering enhanced adaptability. However, a fundamental gap remains: a comprehensive framework unifying these two strategies is still absent, limiting theoretical insights into the filtering paradigms. Moreover, through the lens of Contextual Stochastic Block Model, we reveal that a synthesis of graph-wise and node-wise filtering provides a sufficient solution for classification on graphs exhibiting both homophily and heterophily, suggesting the risk of excessive parameterization and potential overfitting with node-wise filtering. To address the limitations, this paper introduces Coarsening-guided Partition-wise Filtering (CPF). CPF innovates by performing filtering on node partitions. The method begins with structure-aware partition-wise filtering, which filters node partitions obtained via graph coarsening algorithms, and then performs feature-aware partition-wise filtering, refining node embeddings via filtering on clusters produced by $k$-means clustering over features. In-depth analysis is conducted for each phase of CPF, showing its superiority over other paradigms. Finally, benchmark node classification experiments, along with a real-world graph anomaly detection application, validate CPF's efficacy and practical utility.
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