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Spectral-Graph-Survey

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- models.py
- models_multilayer.py
- pyg.py
- pyg_multilayer.py
- readme.md
.DS_Store
CIKM 24 tutorial.pdf
CVPR 24 tutorial.pdf
MDS 24 tutorial.pdf
README.md

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# Awesome Spectral Graph Neural Networks
![PRs Welcome](https://img.shields.io/badge/PRs-Welcome-green) [![Awesome](https://awesome.re/badge.svg)](https://awesome.re)

# Contents

- [Survey Papers](#surveypapers)
- [Milestone Papers](#milestone)
- [Spatial and Spectral Views](#ssviews)
- [Twin Papers](#twinpaper)
- [Applications](#application)
- [Code](#code)
- [Citation](#citation)

# Surveys
- [**Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks.**](https://dl.acm.org/doi/10.1145/3627816)
  - 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.**](https://arxiv.org/abs/2302.05631)
  - 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.**](https://jmlr.csail.mit.edu/papers/volume22/20-213/20-213.pdf)
  - 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.**](https://ieeexplore.ieee.org/abstract/document/7974879?casa_token=Iv5s9xtE6MUAAAAA:hR_rGY3paXXYxbGK_Zg5TMAwIVildEIcnZ9FOrJwtO3Psm3v9k13sU-bvEDzxN1SH_3BuD7S)
  - 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.**](https://ieeexplore.ieee.org/abstract/document/9794480)
  - 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.**](https://normandie-univ.hal.science/hal-02515637v1/file/DSGCN.pdf)
  - Balcilar, Muhammet, Guillaume Renton, Pierre Héroux, Benoit Gauzere, Sebastien Adam, Paul Honeine.
  - arXiv preprint arXiv:2003.11702 (2020).
- [**Understanding spectral graph neural network.**](https://arxiv.org/pdf/2012.06660.pdf)
  -  Chen, Xinye.
  -  arXiv preprint arXiv:2012.06660 (2020).

# Milestone Papers in Building Spectral Graph Convolution
- [Wavelets on graphs via spectral graph theory](https://www.sciencedirect.com/science/article/pii/S1063520310000552)
  - David K. Hammond, Pierre Vandergheynst, Rémi Gribonval,
  - Applied and Computational Harmonic Analysis, 2010
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://proceedings.neurips.cc/paper_files/paper/2016/hash/04df4d434d481c5bb723be1b6df1ee65-Abstract.html)
  - 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](https://ieeexplore.ieee.org/abstract/document/6494675?casa_token=y16k8pzsD00AAAAA:okAjDWZ6nQr4s-rynKsUtem5Tmdb2txXmhL_NAC2p1ggJDCtUFdE0MlKt_9FfVW7t6cjMo5o)
  - 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](https://proceedings.neurips.cc/paper_files/paper/2012/hash/512c5cad6c37edb98ae91c8a76c3a291-Abstract.html), [DeepWalk](https://dl.acm.org/doi/abs/10.1145/2623330.2623732), [LINE](https://arxiv.org/abs/1503.03578)                                                                                                                                                                                                             | [Spectral GNN](https://arxiv.org/abs/1312.6203), [ISGNN](https://arxiv.org/abs/1506.05163), [Neural graph fingerprints](https://proceedings.neurips.cc/paper_files/paper/2015/hash/f9be311e65d81a9ad8150a60844bb94c-Abstract.html)                                                                              |
| 2016        | [DCNN](https://proceedings.neurips.cc/paper_files/paper/2016/hash/390e982518a50e280d8e2b535462ec1f-Abstract.html), [Molecular Graph Convolutions](https://link.springer.com/article/10.1007/s10822-016-9938-8), [PATCHY-SAN](http://proceedings.mlr.press/v48/niepert16)                   | [GCN](https://arxiv.org/abs/1609.02907), [ChebNet](https://proceedings.neurips.cc/paper_files/paper/2016/hash/04df4d434d481c5bb723be1b6df1ee65-Abstract.html)                                                                                                                                                                                                                                              |
| 2017        | [MPNN](https://arxiv.org/abs/1704.01212), [PGCN](https://proceedings.neurips.cc/paper/2017/hash/f507783927f2ec2737ba40afbd17efb5-Abstract.html), [GraphSAGE](https://proceedings.neurips.cc/paper_files/paper/2017/hash/5dd9db5e033da9c6fb5ba83c7a7ebea9-Abstract.html)                                                                                                                                                                                                                                                                                          | [MoNet](https://openaccess.thecvf.com/content_cvpr_2017/html/Monti_Geometric_Deep_Learning_CVPR_2017_paper.html)                                                                                                                                                                                                                                                                                       |
| 2018        | [GIN](https://arxiv.org/abs/1810.00826), [Adaptive GCN](https://proceedings.neurips.cc/paper_files/paper/2018/hash/01eee509ee2f68dc6014898c309e86bf-Abstract.html), [Fast GCN](https://arxiv.org/abs/1801.10247) , [JKNet](http://proceedings.mlr.press/v80/xu18c.html), [Large Scale GCN](https://dl.acm.org/doi/abs/10.1145/3219819.3219947)                                                                                                                                                                                                                        | [RationalNet](https://ieeexplore.ieee.org/abstract/document/8594830), [AR](https://ojs.aaai.org/index.php/AAAI/article/view/11604), [CayleyNet](https://ieeexplore.ieee.org/abstract/document/8521593), [Deep Insights](https://ojs.aaai.org/index.php/AAAI/article/view/11604)                                                                                                          |
| 2019        | [SGCN](https://proceedings.mlr.press/v97/wu19e.html), [DeepGCN](https://openaccess.thecvf.com/content_ICCV_2019/html/Li_DeepGCNs_Can_GCNs_Go_As_Deep_As_CNNs_ICCV_2019_paper.html), [MixHop](http://proceedings.mlr.press/v97/abu-el-haija19a.html), [PPAP](https://arxiv.org/abs/1810.05997)                                                                                                                                                                                                                                                               | [ARMA](https://ieeexplore.ieee.org/abstract/document/9336270), [GDC](https://proceedings.neurips.cc/paper_files/paper/2019/hash/23c894276a2c5a16470e6a31f4618d73-Abstract.html), [EigenPool](https://dl.acm.org/doi/abs/10.1145/3292500.3330982), [GWNN](https://arxiv.org/abs/1904.07785), [Stable GCNN](https://dl.acm.org/doi/abs/10.1145/3292500.3330956)      |
| 2020        | [SIGN](https://arxiv.org/abs/2004.11198), [Spline GNN](https://ojs.aaai.org/index.php/AAAI/article/view/6185), [UaGGP](https://ojs.aaai.org/index.php/AAAI/article/view/5934), [GraLSP](https://ojs.aaai.org/index.php/AAAI/article/view/5861), [GraphSAINT](https://arxiv.org/abs/1907.04931), [DropEdge](https://arxiv.org/abs/1907.10903), [BGNN](https://arxiv.org/abs/2002.03575), [ALaGNN](https://dl.acm.org/doi/abs/10.5555/3491440.3491621), [Continuous GNN](http://proceedings.mlr.press/v119/xhonneux20a.html), [GCNII](https://proceedings.mlr.press/v119/chen20v.html), [PPRGo](https://dl.acm.org/doi/abs/10.1145/3394486.3403296), [DAGNN](https://dl.acm.org/doi/abs/10.1145/3394486.3403076), [H2GCN](https://proceedings.neurips.cc/paper/2020/hash/58ae23d878a47004366189884c2f8440-Abstract.html) | [GraphZoom](https://arxiv.org/abs/1910.02370)                                                                                                                                                                                                                                  |
| 2021        | [ADC](https://proceedings.neurips.cc/paper/2021/hash/c42af2fa7356818e0389593714f59b52-Abstract.html), [UGCN](https://proceedings.neurips.cc/paper_files/paper/2021/hash/5857d68cd9280bc98d079fa912fd6740-Abstract.html), [DGC](https://proceedings.neurips.cc/paper/2021/hash/2d95666e2649fcfc6e3af75e09f5adb9-Abstract.html), [E(n)GNN](https://proceedings.mlr.press/v139/satorras21a.html), [GRAND](http://proceedings.mlr.press/v139/chamberlain21a.html), [C\&S](https://arxiv.org/abs/2010.13993), [LGNN](https://arxiv.org/abs/2110.14322)                                                                                                                                                                                          | [Interpretable Spectral Filter](http://proceedings.mlr.press/v139/kenlay21a.html), [Expressive Spectral Perspective](https://openreview.net/forum?id=-qh0M9XWxnv), [S2GC](https://openreview.net/forum?id=CYO5T-YjWZV), [BernNet](https://proceedings.neurips.cc/paper_files/paper/2021/hash/76f1cfd7754a6e4fc3281bcccb3d0902-Abstract.html), [SpGAT](https://dl.acm.org/doi/abs/10.1145/3459637.3482187)                                                                                                                                                 |
| 2022        | [GINR](https://proceedings.neurips.cc/paper_files/paper/2022/hash/c44a04289beaf0a7d968a94066a1d696-Abstract-Conference.html), [Adaptive SGC](https://proceedings.neurips.cc/paper_files/paper/2022/hash/ae07d152c51ea2ddae65aa7192eb5ff7-Abstract-Conference.html), [PGGNN](https://proceedings.mlr.press/v162/huang22l.html), [DIMP](https://ojs.aaai.org/index.php/AAAI/article/view/20353)                                                                                                                                                                                                                                                                        | [AGWN](https://epubs.siam.org/doi/abs/10.1137/1.9781611977172.12), [ChebNetII](https://proceedings.neurips.cc/paper_files/paper/2022/hash/2f9b3ee2bcea04b327c09d7e3145bd1e-Abstract-Conference.html), [JacobiConv](https://proceedings.mlr.press/v162/wang22am.html), [SpecGNN](https://proceedings.mlr.press/v162/yang22n.html), [G2CN](https://proceedings.mlr.press/v162/li22h.html), [pGNN](https://proceedings.mlr.press/v162/fu22e.html), [ChebGibbsNet](https://openreview.net/forum?id=2a5Ru3JtNe0), [SpecFormer](https://arxiv.org/abs/2303.01028), [SIGN](https://arxiv.org/abs/2202.13013), [Spectral Density](https://dl.acm.org/doi/abs/10.1145/3488560.3498480), [EvenNet](https://proceedings.neurips.cc/paper_files/paper/2022/hash/1e62dae07279cb09d2e87378d10dacfc-Abstract-Conference.html), [MSGNN](https://proceedings.mlr.press/v198/he22c.html)  |
| 2023        | [RSGNN](https://dl.acm.org/doi/abs/10.1145/3543507.3583221), [CAGCN](https://dl.acm.org/doi/abs/10.1145/3543507.3583229), [Low Rank GNN](https://dl.acm.org/doi/abs/10.1145/3543507.3583419), [Auto-HeG](https://arxiv.org/abs/2302.12357), [DropMessage](https://ojs.aaai.org/index.php/AAAI/article/view/25545)                                                                                                                                                                                                                                        | [DSF](https://dl.acm.org/doi/abs/10.1145/3543507.3583324), [F-SEGA](https://dl.acm.org/doi/abs/10.1145/3543507.3583423), [MidGCN](https://dl.acm.org/doi/abs/10.1145/3543507.3583335), [GHRN](https://dl.acm.org/doi/abs/10.1145/3543507.3583268)                                                                                                                                                                                                                  |

# Twin Papers

| Spatial Domain                                                                                                                                                                                                                                                                                                                                                                           | Spectral Domain                                                                                                                                                                                                                                                                                                        |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|       [ Simplifying Graph Convolutional Networks](https://proceedings.mlr.press/v97/wu19e.html) | [Simple Spectral Graph Convolution](https://openreview.net/forum?id=CYO5T-YjWZV)  | 
|[How Powerful are Graph Neural Networks?](https://openreview.net/forum?id=ryGs6iA5Km&noteId=rkl2Q1Qi6X&noteId=rkl2Q1Qi6X), [How Powerful are K-hop Message Passing Graph Neural Networks?](https://proceedings.neurips.cc/paper_files/paper/2022/hash/1ece70d2259b8e9510e2d4ca8754cecf-Abstract-Conference.html)| [How Powerful are Spectral Graph Neural Networks?](https://proceedings.mlr.press/v162/wang22am.html)|
| [Graphon neural networks and the transferability of graph neural networks](https://proceedings.neurips.cc/paper/2020/hash/12bcd658ef0a540cabc36cdf2b1046fd-Abstract.html)   | [Transferability of spectral graph convolutional neural networks](https://jmlr.csail.mit.edu/papers/volume22/20-213/20-213.pdf), [Transferability properties of graph neural networks](https://ieeexplore.ieee.org/abstract/document/10190182)  | 
| [SpatialFormer](https://arxiv.org/pdf/2303.09281.pdf) _CV paper_ | [Specformer](https://arxiv.org/abs/2303.01028) |
| [When Does A Spectral Graph Neural Network Fail in Node Classification?](https://arxiv.org/abs/2202.07902) | [When Does A Spectral Graph Neural Network Fail in Node Classification?](https://arxiv.org/abs/2202.07902) |

# 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}
}
```

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