mlsanityData to 14 Oct 2026

Node-oriented Spectral Filtering for Graph Neural Networks

arXiv 2212.03654 ↗First posted 7 Dec 2022cs.LG cs.SIcited by 17

Not on the map. Why?

Abstract (arXiv)

Graph neural networks (GNNs) have shown remarkable performance on homophilic graph data while being far less impressive when handling non-homophilic graph data due to the inherent low-pass filtering property of GNNs. In general, since real-world graphs are often complex mixtures of diverse subgraph patterns, learning a universal spectral filter on the graph from the global perspective as in most current works may still suffer from great difficulty in adapting to the variation of local patterns. On the basis of the theoretical analysis of local patterns, we rethink the existing spectral filtering methods and propose the node-oriented spectral filtering for graph neural network (namely NFGNN). By estimating the node-oriented spectral filter for each node, NFGNN is provided with the capability of precise local node positioning via the generalized translated operator, thus discriminating the variations of local homophily patterns adaptively. Meanwhile, the utilization of re-parameterization brings a good trade-off between global consistency and local sensibility for learning the node-oriented spectral filters. Furthermore, we theoretically analyze the localization property of NFGNN, demonstrating that the signal after adaptive filtering is still positioned around the corresponding node. Extensive experimental results demonstrate that the proposed NFGNN achieves more favorable performance.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 49 of its 75 references that are in the map. First posted on arXiv 7 Dec 2022.

Builds on

49 of 75 references.

References · 49

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  3. 2017Graph Attention Networkscited by 8,923
  4. 2017Inductive Representation Learning on Large Graphscited by 6,320
  5. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,163
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  7. 2019Simplifying Graph Convolutional Networkscited by 1,477
  8. 2018Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognitioncited by 1,209
  9. 2020LightGCN: Simplifying and Powering Graph Convolution Network for Recommendationcited by 1,139
  10. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,102
  11. 2018Pitfalls of Graph Neural Network Evaluationcited by 1,007
  12. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 993
37 more
  1. 2020Simple and Deep Graph Convolutional Networkscited by 860
  2. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 826
  3. 2019Neural Graph Collaborative Filteringcited by 661
  4. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  5. 2019Multi-scale Attributed Node Embeddingcited by 548
  6. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 443
  7. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 413
  8. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 362
  9. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 311
  10. 2020Towards Deeper Graph Neural Networkscited by 296
  11. 2015Deep Convolutional Networks on Graph-Structured Datacited by 246
  12. 2017struc2vec: Learning Node Representations from Structural Identitycited by 215
  13. 2020Graph Neural Networks with Heterophilycited by 202
  14. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  15. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
  16. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  17. 2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
  18. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  19. 2021Graph-less Neural Networks: Teaching Old MLPs New Tricks via Distillationcited by 152
  20. 2019Graph Wavelet Neural Networkcited by 131
  21. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  22. 2019Stability Properties of Graph Neural Networkscited by 127
  23. 2020Graphon Neural Networks and the Transferability of Graph Neural Networkscited by 118
  24. 2018Large-Scale Learnable Graph Convolutional Networkscited by 113
  25. 2016Community detection in networks: A user guidecited by 105
  26. 2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
  27. 2020Non-Local Graph Neural Networkscited by 91
  28. 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
  29. 2021New Benchmarks for Learning on Non-Homophilous Graphscited by 81
  30. 2021How Framelets Enhance Graph Neural Networkscited by 46
  31. 2021AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filtercited by 43
  32. 2017Spectral Graph Convolutions for Population-based Disease Predictioncited by 42
  33. 2019InceptionGCN: Receptive Field Aware Graph Convolutional Network for Disease Predictioncited by 39
  34. 2022Multi-modal Graph Learning for Disease Predictioncited by 34
  35. 2021Block Modeling-Guided Graph Convolutional Neural Networkscited by 32
  36. 2013Vertex-Frequency Analysis on Graphscited by 25
  37. 2021Powerful Graph Convolutioal Networks with Adaptive Propagation Mechanism for Homophily and Heterophilycited by 14

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 7; 2026: 4.

17 papers.

Sort:

  1. 2023Towards Expressive Spectral-Temporal Graph Neural Networks for Time Series Forecastingcited by 8
  2. 2024SiGNN: A Spike-induced Graph Neural Network for Dynamic Graph Representation Learningcited by 8
  3. 2023Clarify Confused Nodes via Separated Learningcited by 5
  4. 2024Spectral GNN via Two-dimensional (2-D) Graph Convolutioncited by 3
  5. 2024Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learningcited by 3
  6. 2026Complementarity-Supervised Spectral-Band Routing for Multimodal Emotion Recognitioncited by 3
  7. 2025ScaleGNN: Towards Scalable Graph Neural Networks via Adaptive High-order Neighboring Feature Fusioncited by 2
  8. 2025Addressing Noise and Stochasticity in Fraud Detection for Service Networkscited by 2
  9. 2025Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equationscited by 2
  10. 2025Federated Prototype Graph Learningcited by 1
  11. 2025Piecewise Constant Spectral Graph Neural Networkcited by 1
  12. 2024GSpect: Spectral Filtering for Cross-Scale Graph Classificationcited by 0
5 more
  1. 2025Graph Neural Network-based Spectral Filtering Mechanism for Imbalance Classification in Network Digital Twincited by 0
  2. 2025Towards Pre-trained Graph Condensation via Optimal Transportcited by 0
  3. 2026Gate the Filter, Not the Message: Node-Channel Mixtures for Pre-Propagation GNNscited by 0
  4. 2026SMGFM: Spectral Multimodal Graph Pretraining for Multimodal-Attributed Graphscited by 0
  5. 2026Feature Transformation Enhanced Jacobi Polynomial Graph Filtering for Graph Anomaly Detectioncited by 0