# Node-oriented Spectral Filtering for Graph Neural Networks

arXiv: https://arxiv.org/abs/2212.03654 · HTML: https://mlsanity.com/paper/2212.03654/

## 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 (most cited first, 30 of 49)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [How Powerful are Spectral Graph Neural Networks](https://mlsanity.com/paper/2205.11172/) (2022)

## Built on by (most cited first, 17 of 17)

- [Towards Expressive Spectral-Temporal Graph Neural Networks for Time Series Forecasting](https://mlsanity.com/paper/2305.06587/) (2023)
- [SiGNN: A Spike-induced Graph Neural Network for Dynamic Graph Representation Learning](https://mlsanity.com/paper/2404.07941/) (2024)
- [Clarify Confused Nodes via Separated Learning](https://mlsanity.com/paper/2306.02285/) (2023)
- [Spectral GNN via Two-dimensional (2-D) Graph Convolution](https://mlsanity.com/paper/2404.04559/) (2024)
- [Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learning](https://mlsanity.com/paper/2409.09888/) (2024)
- [Complementarity-Supervised Spectral-Band Routing for Multimodal Emotion Recognition](https://mlsanity.com/paper/2603.13340/) (2026)
- [ScaleGNN: Towards Scalable Graph Neural Networks via Adaptive High-order Neighboring Feature Fusion](https://mlsanity.com/paper/2504.15920/) (2025)
- [Addressing Noise and Stochasticity in Fraud Detection for Service Networks](https://mlsanity.com/paper/2505.00946/) (2025)
- [Hyperbolic-PDE GNN: Spectral Graph Neural Networks in the Perspective of A System of Hyperbolic Partial Differential Equations](https://mlsanity.com/paper/2505.23014/) (2025)
- [Federated Prototype Graph Learning](https://mlsanity.com/paper/2504.09493/) (2025)
- [Piecewise Constant Spectral Graph Neural Network](https://mlsanity.com/paper/2505.04808/) (2025)
- [GSpect: Spectral Filtering for Cross-Scale Graph Classification](https://mlsanity.com/paper/2409.00338/) (2024)
- [Graph Neural Network-based Spectral Filtering Mechanism for Imbalance Classification in Network Digital Twin](https://mlsanity.com/paper/2502.11505/) (2025)
- [Towards Pre-trained Graph Condensation via Optimal Transport](https://mlsanity.com/paper/2509.14722/) (2025)
- [Gate the Filter, Not the Message: Node-Channel Mixtures for Pre-Propagation GNNs](https://mlsanity.com/paper/2606.01660/) (2026)
- [SMGFM: Spectral Multimodal Graph Pretraining for Multimodal-Attributed Graphs](https://mlsanity.com/paper/2606.12867/) (2026)
- [Feature Transformation Enhanced Jacobi Polynomial Graph Filtering for Graph Anomaly Detection](https://mlsanity.com/paper/2608.27144/) (2026)

## 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.