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Rethinking the Graph Polynomial Filter via Positive and Negative Coupling Analysis

arXiv 2404.10353 ↗First posted 16 Apr 2024cs.LG cs.SIcited by 0

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Abstract (arXiv)

Recently, the optimization of polynomial filters within Spectral Graph Neural Networks (GNNs) has emerged as a prominent research focus. Existing spectral GNNs mainly emphasize polynomial properties in filter design, introducing computational overhead and neglecting the integration of crucial graph structure information. We argue that incorporating graph information into basis construction can enhance understanding of polynomial basis, and further facilitate simplified polynomial filter design. Motivated by this, we first propose a Positive and Negative Coupling Analysis (PNCA) framework, where the concepts of positive and negative activation are defined and their respective and mixed effects are analysed. Then, we explore PNCA from the message propagation perspective, revealing the subtle information hidden in the activation process. Subsequently, PNCA is used to analyze the mainstream polynomial filters, and a novel simple basis that decouples the positive and negative activation and fully utilizes graph structure information is designed. Finally, a simple GNN (called GSCNet) is proposed based on the new basis. Experimental results on the benchmark datasets for node classification verify that our GSCNet obtains better or comparable results compared with existing state-of-the-art GNNs while demanding relatively less computational time.

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References · 22

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  3. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,089
  4. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  5. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 877
  6. 2020Simple and Deep Graph Convolutional Networkscited by 860
  7. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 595
  8. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 311
  9. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  10. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  11. 2018Traffic Graph Convolutional Recurrent Neural Network: A Deep Learning Framework for Network-Scale Traffic Learning and Forecastingcited by 146
  12. 2018Contextual Stochastic Block Modelscited by 134
10 more
  1. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  2. 2018DeepInf: Social Influence Prediction with Deep Learningcited by 128
  3. 2020Revisiting Graph based Collaborative Filtering: A Linear Residual Graph Convolutional Network Approachcited by 120
  4. 2022Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisitedcited by 87
  5. 2021Generalizing Graph Neural Networks on Out-Of-Distribution Graphscited by 71
  6. 2022A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networkscited by 49
  7. 2022RAW-GNN: RAndom Walk Aggregation based Graph Neural Networkcited by 25
  8. 2023A Neural Collapse Perspective on Feature Evolution in Graph Neural Networkscited by 19
  9. 2021Learning Graph Neural Networks with Positive and Unlabeled Nodescited by 11
  10. 2021Enhance Information Propagation for Graph Neural Network by Heterogeneous Aggregationscited by 6

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