Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918029716094976 |
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| author | Li, Guoming Yang, Jian Chen, Yifan |
| author_facet | Li, Guoming Yang, Jian Chen, Yifan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening Li, Guoming Yang, Jian Chen, Yifan Machine Learning Numerical Analysis Signal Processing 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. |
| title | Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening |
| topic | Machine Learning Numerical Analysis Signal Processing |
| url | https://arxiv.org/abs/2505.14033 |