Awesome Spectral Graph Neural Networks

Contents

• Survey Papers
• Milestone Papers
• Spatial and Spectral Views
• Twin Papers
• Applications
• Code
• Citation

Surveys

• Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks.
  • Zhiqian Chen, Fanglan Chen, Lei Zhang, Taoran Ji, Kaiqun Fu, Liang Zhao, Feng Chen, Lingfei Wu, Charu Aggarwal, Chang-Tien Lu.
  • ACM Computer Surveys (CSUR), 2023
• A Survey on Spectral Graph Neural Networks.
  • Bo, Deyu, Xiao Wang, Yang Liu, Yuan Fang, Yawen Li, and Chuan Shi.
  • arXiv preprint arXiv:2302.05631 (2023)
• Transferability of spectral graph convolutional neural networks.
  • Levie, Ron, Wei Huang, Lorenzo Bucci, Michael Bronstein, and Gitta Kutyniok.
  • The Journal of Machine Learning Research (JMLR) 22, no. 1 (2021): 12462-12520.
• Geometric deep learning: going beyond euclidean data.
  • Bronstein, Michael M., Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst.
  • IEEE Signal Processing Magazine (SPM) 34, no. 4 (2017): 18-42.
• Spectral Graph Convolutional Neural Networks in the Context of Regularization Theory.
  • A. Salim and S. Sumitra
  • IEEE Transactions on Neural Networks and Learning Systems (TNNLS), 2022
• Bridging the gap between spectral and spatial domains in graph neural networks.
  • Balcilar, Muhammet, Guillaume Renton, Pierre Héroux, Benoit Gauzere, Sebastien Adam, Paul Honeine.
  • arXiv preprint arXiv:2003.11702 (2020).
• Understanding spectral graph neural network.
  • Chen, Xinye.
  • arXiv preprint arXiv:2012.06660 (2020).

Milestone Papers in Building Spectral Graph Convolution

• Wavelets on graphs via spectral graph theory
  • David K. Hammond, Pierre Vandergheynst, Rémi Gribonval,
  • Applied and Computational Harmonic Analysis, 2010
• Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
  • Michaël Defferrard, Xavier Bresson, Pierre Vandergheynst
  • Advances in Neural Information Processing Systems (NIPS), 2016
• The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
  • D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega and P. Vandergheynst
  • IEEE Signal Processing Magazine, 2013

GNNs in Spatial and Spectral Views

Year	Spatial Domain	Spectral Domain
Before 2015	ParWalk, DeepWalk, LINE	Spectral GNN, ISGNN, Neural graph fingerprints
2016	DCNN, Molecular Graph Convolutions, PATCHY-SAN	GCN, ChebNet
2017	MPNN, PGCN, GraphSAGE	MoNet
2018	GIN, Adaptive GCN, Fast GCN , JKNet, Large Scale GCN	RationalNet, AR, CayleyNet, Deep Insights
2019	SGCN, DeepGCN, MixHop, PPAP	ARMA, GDC, EigenPool, GWNN, Stable GCNN
2020	SIGN, Spline GNN, UaGGP, GraLSP, GraphSAINT, DropEdge, BGNN, ALaGNN, Continuous GNN, GCNII, PPRGo, DAGNN, H2GCN	GraphZoom
2021	ADC, UGCN, DGC, E(n)GNN, GRAND, C&S, LGNN	Interpretable Spectral Filter, Expressive Spectral Perspective, S2GC, BernNet, SpGAT
2022	GINR, Adaptive SGC, PGGNN, DIMP	AGWN, ChebNetII, JacobiConv, SpecGNN, G2CN, pGNN, ChebGibbsNet, SpecFormer, SIGN, Spectral Density, EvenNet, MSGNN
2023	RSGNN, CAGCN, Low Rank GNN, Auto-HeG, DropMessage	DSF, F-SEGA, MidGCN, GHRN

Twin Papers

Spatial Domain	Spectral Domain
Simplifying Graph Convolutional Networks	Simple Spectral Graph Convolution
How Powerful are Graph Neural Networks?, How Powerful are K-hop Message Passing Graph Neural Networks?	How Powerful are Spectral Graph Neural Networks?
Graphon neural networks and the transferability of graph neural networks	Transferability of spectral graph convolutional neural networks, Transferability properties of graph neural networks
SpatialFormer CV paper	Specformer
When Does A Spectral Graph Neural Network Fail in Node Classification?	When Does A Spectral Graph Neural Network Fail in Node Classification?

Applications with Spectral Graph

• "Graph frequency analysis of brain signals."
  • Huang, Weiyu, Leah Goldsberry, Nicholas F. Wymbs, Scott T. Grafton, Danielle S. Bassett, and Alejandro Ribeiro.
  • IEEE journal of selected topics in signal processing 10, no. 7 (2016): 1189-1203.
• "Spectral graph convolutions for population-based disease prediction."
  • Parisot, Sarah, Sofia Ira Ktena, Enzo Ferrante, Matthew Lee, Ricardo Guerrerro Moreno, Ben Glocker, and Daniel Rueckert.
  • In Medical Image Computing and Computer Assisted Intervention− MICCAI 2017: 20th International Conference, Quebec City, QC, Canada, September 11-13, 2017, Proceedings, Part III 20, pp. 177-185. Springer International Publishing, 2017.
• "Disease prediction using graph convolutional networks: application to autism spectrum disorder and Alzheimer’s disease."
  • Parisot, Sarah, Sofia Ira Ktena, Enzo Ferrante, Matthew Lee, Ricardo Guerrerro Moreno, Ben Glocker, and Daniel Rueckert.
  • Medical image analysis 48 (2018): 117-130.
• "Spectral graph theory of brain oscillations."
  • Raj, Ashish, Chang Cai, Xihe Xie, Eva Palacios, Julia Owen, Pratik Mukherjee, and Srikantan Nagarajan.
  • Human brain mapping 41, no. 11 (2020): 2980-2998.
• "Spectral graph theory of brain oscillations—-Revisited and improved."
  • Verma, Parul, Srikantan Nagarajan, and Ashish Raj.
  • NeuroImage 249 (2022): 118919.
• "A spectral graph regression model for learning brain connectivity of Alzheimer’s disease."
  • Hu, Chenhui, Lin Cheng, Jorge Sepulcre, Keith A. Johnson, Georges E. Fakhri, Yue M. Lu, and Quanzheng Li.
  • PloS one 10, no. 5 (2015): e0128136.
• "Stability and dynamics of a spectral graph model of brain oscillations."
  • Hu, Chenhui, Lin Cheng, Jorge Sepulcre, Keith A. Johnson, Georges E. Fakhri, Yue M. Lu, and Quanzheng Li.
  • Network Neuroscience 7, no. 1 (2023): 48-72.
• "Learning spectral graph transformations for link prediction."
  • Kunegis, Jérôme, and Andreas Lommatzsch.
  • In Proceedings of the 26th Annual International Conference on Machine Learning, pp. 561-568. 2009.
• "Spectral graph analysis of the geometry of power flows in transmission networks."
  • Retiére, Nicolas, Dinh Truc Ha, and Jean-Guy Caputo.
  • IEEE Systems Journal 14, no. 2 (2019): 2736-2747.
• "Threshold selection in gene co-expression networks using spectral graph theory techniques."
  • Perkins, Andy D., and Michael A. Langston.
  • In BMC bioinformatics, vol. 10, no. 11, pp. 1-11. BioMed Central, 2009.
• "Graph spectral analysis of protein interaction network evolution."
  • Thorne, Thomas, and Michael PH Stumpf.
  • Journal of The Royal Society Interface 9, no. 75 (2012): 2653-2666.
• "Investigating transport network vulnerability by capacity weighted spectral analysis."
  • Bell, Michael GH, Fumitaka Kurauchi, Supun Perera, and Walter Wong.
  • Transportation Research Part B: Methodological 99 (2017): 251-266.
• "Spectral graph convolutions for population-based disease prediction."
  • Parisot, Sarah, Sofia Ira Ktena, Enzo Ferrante, Matthew Lee, Ricardo Guerrerro Moreno, Ben Glocker, and Daniel Rueckert.
  • In Medical Image Computing and Computer Assisted Intervention− MICCAI 2017: 20th International Conference, Quebec City, QC, Canada, September 11-13, 2017, Proceedings, Part III 20, pp. 177-185. Springer International Publishing, 2017.
• "Epidemic spreading in real networks: An eigenvalue viewpoint."
  • Wang, Yang, Deepayan Chakrabarti, Chenxi Wang, and Christos Faloutsos.
  • In 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings., pp. 25-34. IEEE, 2003.

Experiment Code for Benchmarking Rational vs Polynomial

See code folder

Citation Info

@article{10.1145/3627816,
    author = {Chen, Zhiqian and Chen, Fanglan and Zhang, Lei and Ji, Taoran and Fu, Kaiqun and Zhao, Liang and Chen, Feng and Wu, Lingfei and Aggarwal, Charu and Lu, Chang-Tien},
    title = {Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks},
    year = {2023},
    issue_date = {May 2024},
    publisher = {Association for Computing Machinery},
    address = {New York, NY, USA},
    volume = {56},
    number = {5},
    issn = {0360-0300},
    url = {https://doi.org/10.1145/3627816},
    doi = {10.1145/3627816},
    journal = {ACM Comput. Surv.},
    month = {dec},
    articleno = {126},
    numpages = {42},
    keywords = {approximation theory, spectral graph theory, Deep learning, graph neural networks, graph learning}
}