基于自适应组合滤波器的谱图神经网络

doi:10.16451/j.cnki.issn1003-6059.202412003

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Abstract Spectral graph neural networks(SGNNs) exhibit strong performance in processing homophilic graph data. However, most existing SGNNs design filters based on polynomial approximations of Laplacian matrix, which struggle to effectively capture high-frequency components of graph signals. Consequently, their performance on heterophilic graphs is limited. Additionally, filters based on Laplacian matrix can only capture global structural features of graph topology, limiting their adaptability to complex local patterns in graph data. To overcome these limitations, a spectral graph neural network based on adaptive combination filters(ACGNN) is proposed. Instead of using polynomial bases, eigenvectors and eigenvalues of Laplacian matrix are combined to design a filter by partitioning node neighborhood patterns, and the filter can effectively capture and learn diverse node neighborhood structural patterns. Moreover, the filter can adaptively adjust weights based on node characteristics by integrating a parameter matrix associated with node features into the filter function. Experimental results on both homophilic and heterophilic graph datasets validate the effectiveness and superior performance of ACGNN.

Key words： Spectral Graph Neural Network Heterophilic Graph Combination Filters Node Classification

Received: 23 September 2024

ZTFLH:

TP 391

Fund:National Natural Science Foundation of China(No.12271235), Natural Science Foundation of Fujian Province(No.2021J06029), Science and Technology Project of Minnan Normal University(No.KJ2021020), High-Level Cultivation Pro-ject of Minnan Normal University(No.MSGJB2022010)

Corresponding Authors: HUANG Meixiang, Ph.D., lecturer. Her research interests include image processing and deep lear-ning.

About author:: LI Weinuo, Master student. His research interests include machine learning and graph neural network.
LU Fuliang, Ph.D., professor. His research interests include graph theory and applications.
TU Liangping, Ph.D., professor. His research interests include machine learning and artificial intelligence.

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Cite this article:

LI Weinuo,HUANG Meixiang,LU Fuliang等. Spectral Graph Neural Network Based on Adaptive Combination Filters[J]. Pattern Recognition and Artificial Intelligence, 2024, 37(12): 1069-1082.

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http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.202412003 OR http://manu46.magtech.com.cn/Jweb_prai/EN/Y2024/V37/I12/1069

[1] WANG K F, AN J, ZHOU M C, et al. Minority-Weighted Graph Neural Network for Imbalanced Node Classification in Social Networks of Internet of People. IEEE Internet of Things Journal, 2023, 10(1): 330-340.
[2] MIN S J, GAO Z, PENG J, et al. STGSN-A Spatial-Temporal Graph Neural Network Framework for Time-Evolving Social Networks. Knowledge-Based Systems, 2021, 214. DOI: 10.1016/j.knosys.2021.106746.
[3] WU S W, SUN F, ZHANG W T, et al. Graph Neural Networks in Recommender Systems: A Survey. ACM Computing Surveys, 2022, 55(5). DOI: 10.1145/3535101.
[4] XIA L H, HUANG C, XU Y, et al. Multi-behavior Graph Neural Networks for Recommender System. IEEE Transactions on Neural Networks and Learning Systems, 2024, 35(4): 5473-5487.
[5] ZHANG Y Q, YAO Q M, YUE L, et al. Emerging Drug Interaction Prediction Enabled by a Flow-Based Graph Neural Network with Biomedical Network. Nature Computational Science, 2023, 3(12): 1023-1033.
[6] BONGINI P, BIANCHINI M, SCARSELLI F. Molecular Generative Graph Neural Networks for Drug Discovery. Neurocomputing, 2021, 450: 242-252.
[7] ZHAO L, SONG Y J, ZHANG C, et al. T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction. IEEE Transactions on Intelligent Transportation Systems, 2020, 21(9): 3848-3858.
[8] MCPHERSON M, SMITH-LOVIN L, COOK J M. Birds of a Fea-ther: Homophily in Social Networks. Annual Review of Sociology, 2001, 27(1): 415-444.
[9] VON LUXBURG U. A Tutorial on Spectral Clustering. Statistics and Computing, 2007, 17(4): 395-416.
[10] ZHU J, ROSSI R A, RAO A, et al. Graph Neural Networks with Heterophily. Proceedings of the AAAI Conference on Artificial Intelligence, 2021, 35(12): 11168-11176.
[11] PEI H B, WEI B Z, CHANG K C C, et al. Geom-GCN: Geome-tric Graph Convolutional Networks[C/OL]. [2024-08-19]. https://arxiv.org/pdf/2002.05287.
[12] YAN S R, LI C Y, WANG H S, et al. Feature Interactive Graph Neural Network for KG-Based Recommendation. Expert Systems with Applications, 2024, 237. DOI: 10.1016/j.eswa.2023.121411.
[13] ZHENG S, ZHU Z F, LIU Z Z, et al. Node-Oriented Spectral Filtering for Graph Neural Networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024, 46(1): 388-402.
[14] BOJCHEVSKI A, GASTEIGER J, PEROZZI B, et al. Scaling Graph Neural Networks with Approximate PageRank // Proc of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, USA: ACM, 2020: 2464-2473.
[15] GILMER J, SCHOENHOLZ S S, RILEY P F, et al. Neural Me-ssage Passing for Quantum Chemistry // Proc of the 34th International Conference on Machine Learning. San Diego, USA: JMLR, 2017: 1263-1272.
[16] WU Z H, JAIN P, WRIGHT M A, et al. Representing Long-Range Context for Graph Neural Networks with Global Attention // Proc of the 35th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2021: 13266-13279.
[17] ZHANG J W, ZHANG H P, XIA C Y, et al. GRAPH-BERT: Only Attention Is Needed for Learning Graph Representations[C/OL]. [2024-08-19]. https://arxiv.org/pdf/2001.05140.
[18] RONG Y, BIAN Y T, XU T Y, et al. Self-Supervised Graph Trans-former on Large-Scale Molecular Data // Proc of the 34th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2020: 12559-12571.
[19] BRUNA J, ZAREMBA W, SZLAM A, et al. Spectral Networks and Locally Connected Networks on Graphs[C/OL]. [2024-08-19]. https://arxiv.org/pdf/1312.6203.
[20] DEFFERRARD M, BRESSON X, VANDERGHEYNST P. Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering // Proc of the 30th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2016: 3844-3852.
[21] XU B B, SHEN H W, CAO Q, et al. Graph Wavelet Neural Network[C/OL]. [2024-08-19]. https://arxiv.org/pdf/1904.07785.
[22] CHUNG F R K. Spectral Graph Theory. Cambridge, USA: Cambridge University Press, 1997.
[23] ORTEGA A, FROSSARD P, KOVACˇEVIC＇ J, et al. Graph Signal Processing: Overview, Challenges, and Applications. Proceedings of the IEEE, 2018, 106(5): 808-828.
[24] ZHU J, YAN Y J, XHAO L X, et al. Beyond Homophily in Graph Neural Networks: Current Limitations and Effective Designs // Proc of the 34th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2020: 7793-7804.
[25] ABU-EL-HAIJA S, PEROZZI B, KAPOOR A, et al. MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing // Proc of the 36th International Conference on Machine Learning. San Diego, USA: JMLR, 2019: 21-29.
[26] YAN Y J, HASHEMI M, SWERSKY K, et al. Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks // Proc of the IEEE International Conference on Data Mining. Washington, USA: IEEE, 2022: 1287-1292.
[27] LIU M, WANG Z Y, JI S W, et al. Non-local Graph Neural Networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022, 44(12): 10270-10276.
[28] JIN D, YU Z Z, HUO C Y, et al. Universal Graph Convolutional Networks // Proc of the 35th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2021: 10654-10664.
[29] ZHENG X, WANG Y, LIU Y X, et al. Graph Neural Networks for Graphs with Heterophily: A Survey[C/OL]. [2024-08-19]. https://arxiv.org/pdf/2202.07082.
[30] CHIEN E, PENG J H, LI P, et al. Adaptive Universal Genera-lized PageRank Graph Neural Network[C/OL]. [2024-08-19]. https://arxiv.org/pdf/2006.07988.
[31] HE M G, WEI Z W, XU H F. BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation // Proc of the 35th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2021: 14239-14251.
[32] WANG X Y, ZHANG M H. How Powerful Are Spectral Graph Neural Networks // Proc of the 39th International Conference on Machine Learning. San Diego, USA: JMLR, 2022: 23341-23362.
[33] HE M G, WEI Z W, WEN J R. Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited // Proc of the 36th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2022: 7264-7276.
[34] FENG J R, CHEN Y X, LI P H, et al. How Powerful Are k-Hop Message Passing Graph Neural Networks // Proc of the 36th International Conference on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2022: 4776-4790.
[35] YANG Z R, HU Y L, OUYANG S, et al. WaveNet: Tackling Non-stationary Graph Signals via Graph Spectral Wavelets. Proceedings of the AAAI Conference on Artificial Intelligence, 2024, 38(8): 9287-9295.
[36] SHUMAN D I, NARANG S K, FROSSARD P, et al. The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains. IEEE Signal Processing Magazine, 2013, 30(3): 83-98.
[37] DE OLIVEIRA H M, DE SOUZA D F. Wavelet Analysis as an Information Processing Technique // Proc of the International Telecommunications Symposium. Washington, USA: IEEE, 2006: 7-12.
[38] ZHOU D Y, SCHÖLKOPF B. A Regularization Framework for Learning from Graph Data[C/OL]. [2024-08-19]. https://www.microsoft.com/en-us/research/wp-content/uploads/2017/01/RFLG.pdf.
[39] TRICK T. Theory and Application of Digital Signal Processing. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1975, 23(4): 394-395.
[40] BANERJEE A. The Spectrum of the Graph Laplacian as a Tool for Analyzing Structure and Evolution of Networks[C/OL]. [2024-08-19]. https://www.iiserkol.ac.in/~anirban.banerjee/Banerjee_PhD_Thesis.pdf.
[41] SEN P, NAMATA G, BILGIC M, et al. Collective Classification in Network Data. AI Magazine, 2008, 29(3): 93-106.
[42] SHCHUR O, MUMME M, BOJCHEVSKI A, et al. Pitfalls of Graph Neural Network Evaluation[C/OL]. [2024-08-19]. https://arxiv.org/pdf/1811.05868.
[43] ROZEMBERCZKI B, ALLEN C, SARKAR R. Multi-scale Attri-buted Node Embedding[C/OL]. [2024-08-19]. https://openreview.net/pdf?id=HJxiMAVtPH.
[44] KIPF T N, WELLING M. Semi-supervised Classification with Graph Convolutional Networks[C/OL]. [2024-08-19]. https://arxiv.org/pdf/1609.02907.
[45] GASTEIGER J, BOJCHEVSKI A, GÜNNEMANN S. Predict Then Propagate: Graph Neural Networks Meet Personalized Pagerank[C/OL]. [2024-08-19]. https://arxiv.org/pdf/1810.05997.
[46] MA N, GUAN J C, ZHAO Y. Bringing PageRank to the Citation Analysis. Information Processing and Management, 2008, 44(2): 800-810.
[47] VELICKOVIC P, CUCURULL G, CASANOVA A, et al. Graph Attention Networks[C/OL]. [2024-08-19]. https://arxiv.org/pdf/1710.10903.
[48] BO D Y, WANG X, SHI C, et al. Beyond Low-Frequency Information in Graph Convolutional Networks. Proceedings of the AAAI Conference on Artificial Intelligence, 2021, 35(5): 3950-3957.
[49] BODNAR C, DI GIOVANNI F, CHAMBERLAIN B P, et al. Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs // Proc of the 36th International Confe-rence on Neural Information Processing Systems. Cambridge, USA: MIT Press, 2022: 18527-18541.
[50] LIU Y X, ZHENG Y Z, ZHANG D K, et al. Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating. Proceedings of the AAAI Conference on Artificial Intelligence, 2023, 37(4): 4516-4524.
[51] KOESTER G. On 4-Critical Planar Graphs with High Edge Density. Discrete Mathematics, 1991, 98(2): 147-151.
[52] LI Q M, HAN Z C, WU X M. Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning. Proceedings of the AAAI Conference on Artificial Intelligence, 2018, 32(1): 3538-3545.