Abstract
Graph neural networks have emerged as a powerful representation learning model for undertaking various graph prediction tasks. Various graph pooling methods have been developed to coarsen an input graph into a succinct graph-level representation through aggregating node embeddings obtained via graph convolution. However, because most graph pooling methods are heavily node-centric, they fail to fully leverage the crucial information contained in graph structure. This paper presents a cross-view graph pooling method (Co-Pooling) that explicitly exploits crucial graph substructures for learning graph representations. Co-Pooling is designed to fuse the pooled representations from both node view and edge view. Through cross-view interaction, edge-view pooling and node-view pooling mutually reinforce each other to learn informative graph representations. Extensive experiments on one synthetic and 15 real-world graph datasets validate the effectiveness of our Co-Pooling method. Our results and analysis show that (1) our method is able to yield promising results over graphs with various types of node attributes, and (2) our method can achieve superior performance over state-of-the-art pooling methods on graph classification and regression tasks.
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References
Chen, Z., Chen, L., Villar, S., Bruna, J.: Can graph neural networks count substructures? NeurIPS 33, 10383–10395 (2020)
Chien, E., Peng, J., Li, P., Milenkovic, O.: Adaptive universal generalized pagerank graph neural network. In: ICLR (2021)
Diehl, F.: Edge contraction pooling for graph neural networks. arXiv preprint arXiv:1905.10990 (2019)
Dwivedi, V.P., Joshi, C.K., Laurent, T., Bengio, Y., Bresson, X.: Benchmarking graph neural networks. arXiv preprint arXiv:2003.00982 (2020)
Galland, A.: Graph pooling by edge cut (2021)
Gao, H., Ji, S.: Graph u-nets. In: ICML, pp. 2083–2092. PMLR (2019)
Gao, X., Dai, W., Li, C., Xiong, H., Frossard, P.: iPool-information-based pooling in hierarchical graph neural networks. IEEE TNNLS 33, 1–13 (2021)
Hamilton, W.L., Ying, R., Leskovec, J.: Inductive representation learning on large graphs. In: NIPS, pp. 1025–1035 (2017)
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. In: ICLR (2017)
Lee, J., Lee, I., Kang, J.: Self-attention graph pooling. In: ICML, pp. 3734–3743 (2019)
Liu, N., Jian, S., Li, D., Zhang, Y., Lai, Z., Xu, H.: Hierarchical adaptive pooling by capturing high-order dependency for graph representation learning. IEEE TKDE (2021)
Morris, C., Kriege, N., Bause, F., Kersting, K., Mutzel, P., Neumann, M.: Tudataset: a collection of benchmark datasets for learning with graphs. arXiv:2007.08663 (2020)
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298, 824–827 (2002)
Orsini, F., Frasconi, P., De Raedt, L.: Graph invariant kernels. In: IJCAI, pp. 3756–3762 (2015)
Ranjan, E., Sanyal, S., Talukdar, P.: ASAP: adaptive structure aware pooling for learning hierarchical graph representations. In: AAAI, pp. 5470–5477 (2020)
Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo, N., et al. (eds.) SSPR /SPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89689-0_33
Shang, J., et al.: Assembling molecular sierpiński triangle fractals. Nat. Chem. 7(5), 389–393 (2015)
Sun, Q., et al.: Sugar: subgraph neural network with reinforcement pooling and self-supervised mutual information mechanism. In: Proceedings of the Web Conference 2021, pp. 2081–2091 (2021)
Sutherland, J.J., O’brien, L.A., Weaver, D.F.: Spline-fitting with a genetic algorithm: a method for developing classification structure-activity relationships. J. Chem. Inf. Comput. Sci. 43(6), 1906–1915 (2003)
Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. In: ICLR (2018)
Wang, Y.G., Li, M., Ma, Z., Montufar, G., Zhuang, X., Fan, Y.: Haar graph pooling. In: ICML, pp. 9952–9962 (2020)
Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? In: ICLR (2019)
Yanardag, P., Vishwanathan, S.: Deep graph kernels. In: SIGKDD, pp. 1365–1374 (2015)
Ying, R., You, J., Morris, C., Ren, X., Hamilton, W.L., Leskovec, J.: Hierarchical graph representation learning with differentiable pooling. In: NIPS, pp. 4805–4815 (2018)
Yuan, H., Ji, S.: Structpool: structured graph pooling via conditional random fields. In: ICLR (2020)
Zhang, Z., et al.: Hierarchical graph pooling with structure learning. arXiv preprint arXiv:1911.05954 (2019)
Zhang, M., Cui, Z., Neumann, M., Chen, Y.: An end-to-end deep learning architecture for graph classification. In: AAAI, pp. 4438–4445 (2018)
Acknowledgements
Xiaowei Zhou is supported by a Data61 PhD Scholarship from CSIRO. Ivor W. Tsang is supported by the Center for Frontier AI research, A*STAR, and ARC under grants DP200101328. This work is partially supported by the USYD-Data61 Collaborative Research Project grant.
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Zhou, X., Yin, J., Tsang, I.W. (2023). Edge but not Least: Cross-View Graph Pooling. In: Amini, MR., Canu, S., Fischer, A., Guns, T., Kralj Novak, P., Tsoumakas, G. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2022. Lecture Notes in Computer Science(), vol 13714. Springer, Cham. https://doi.org/10.1007/978-3-031-26390-3_21
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