Abstract
Graph pooling is a crucial operation in graph neural networks (GNNs) for down-sampling. It is noted that existing methods for graph pooling suffer from two main issues. First, pooling methods based on node dropping only evaluate the importance of nodes from a single perspective, such as attention or node distance. However, the importance scores of a node are different when evaluating it from different aspects, and thus the importance of a node cannot be evaluated comprehensively only based on one single view. Second, necessary information about graph structure will be lost when nodes with lower scores are discarded. It can even result in the coarsened graph being too sparse and further lead to poor performance in related learning tasks, such as graph classification. To address these issues, we propose an attention-based multi-view parallel graph pooling method. Specifically, to comprehensively evaluate the importance of nodes, we propose to evaluate the importance node from its features, local topology structure, and global topology structure via the attention mechanism. Moreover, to alleviate the problem of information loss caused by node discarding in graph pooling, we introduce the concept of multi-view parallel pooling, which conducts graph pooling from node features, local topology, and global topology structure three views, respectively, and then integrates the three generated coarsened graphs and obtains an informative graph. Experimental results on four benchmark datasets demonstrate the effectiveness of our proposed method for graph classification.
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Data Availability
The experimental datasets are available at https://chrsmrrs.github.io/datasets/docs/datasets/.
References
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)
Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. arXiv preprint arXiv:1710.10903 (2017)
Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? arXiv preprint arXiv:1810.00826 (2018)
Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. Adv. Neural Inf. Process. Syst. 30 (2017)
Schlichtkrull, M., Kipf, T.N., Bloem, P., Van Den Berg, R., Titov, I., Welling, M.: Modeling relational data with graph convolutional networks. In: The Semantic Web: 15th International Conference, ESWC 2018, Heraklion, Crete, Greece, June 3–7, 2018, Proceedings 15, pp. 593–607 (2018). Springer
Smalter, A., Huan, J., Lushington, G.: Graph wavelet alignment kernels for drug virtual screening. J. Bioinform. Comput. Biol. 7(03), 473–497 (2009)
Mahé, P., Vert, J.-P.: Graph kernels based on tree patterns for molecules. Mach. Learn. 75(1), 3–35 (2009)
Duvenaud, D.K., Maclaurin, D., Iparraguirre, J., Bombarell, R., Hirzel, T., Aspuru-Guzik, A., Adams, R.P.: Convolutional networks on graphs for learning molecular fingerprints. Adv. Neural Inf. Process. Syst. 28 (2015)
Ying, Z., You, J., Morris, C., Ren, X., Hamilton, W., Leskovec, J.: Hierarchical graph representation learning with differentiable pooling. Adv. Neural Inf. Process. Syst. 31 (2018)
Lee, J., Lee, I., Kang, J.: Self-attention graph pooling. In: International Conference on Machine Learning, pp. 3734–3743 (2019). PMLR
Gao, H., Ji, S.: Graph u-nets. In: International Conference on Machine Learning, pp. 2083–2092 (2019). PMLR
Zhang, Z., Bu, J., Ester, M., Zhang, J., Yao, C., Yu, Z., Wang, C.: Hierarchical graph pooling with structure learning. arXiv preprint arXiv:1911.05954 (2019)
Gao, H., Liu, Y., Ji, S.: Topology-aware graph pooling networks. IEEE Trans. Pattern Anal. Mach. Intell. 43(12), 4512–4518 (2021)
Henaff, M., Bruna, J., LeCun, Y.: Deep convolutional networks on graph-structured data. arXiv preprint arXiv:1506.05163 (2015)
Bruna, J., Zaremba, W., Szlam, A., LeCun, Y.: Spectral networks and locally connected networks on graphs. arXiv preprint arXiv:1312.6203 (2013)
Navarin, N., Van Tran, D., Sperduti, A.: Universal readout for graph convolutional neural networks. In: 2019 International Joint Conference on Neural Networks (IJCNN), pp. 1–7 (2019). IEEE
Chen, T., Bian, S., Sun, Y.: Are powerful graph neural nets necessary? A dissection on graph classification. arXiv preprint arXiv:1905.04579 (2019)
Papp, P.A., Martinkus, K., Faber, L., Wattenhofer, R.: Dropgnn: Random dropouts increase the expressiveness of graph neural networks. Adv. Neural. Inf. Process. Syst. 34, 21997–22009 (2021)
Fan, X., Gong, M., Xie, Y., Jiang, F., Li, H.: Structured self-attention architecture for graph-level representation learning. Pattern Recogn. 100, 107084 (2020)
Itoh, T.D., Kubo, T., Ikeda, K.: Multi-level attention pooling for graph neural networks: Unifying graph representations with multiple localities. Neural Netw. 145, 356–373 (2022)
Zhang, M., Cui, Z., Neumann, M., Chen, Y.: An end-to-end deep learning architecture for graph classification. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32 (2018)
Bai, L., Jiao, Y., Cui, L., Rossi, L., Wang, Y., Yu, P., Hancock, E.: Learning graph convolutional networks based on quantum vertex information propagation. IEEE Trans. Knowl. Data Eng. (2021)
Wang, Z., Ji, S.: Second-order pooling for graph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. (2020)
Chen, K., Song, J., Liu, S., Yu, N., Feng, Z., Han, G., Song, M.: Distribution knowledge embedding for graph pooling. IEEE Trans. Knowl. Data Eng. (2022)
Vinyals, O., Bengio, S., Kudlur, M.: Order matters: sequence to sequence for sets. arXiv preprint arXiv:1511.06391 (2015)
Yuan, H., Ji, S.: Structpool: Structured graph pooling via conditional random fields. In: Proceedings of the 8th International Conference on Learning Representations (2020)
Noutahi, E., Beaini, D., Horwood, J., Giguère, S., Tossou, P.: Towards interpretable sparse graph representation learning with laplacian pooling. arXiv preprint arXiv:1905.11577 (2019)
Bianchi, F.M., Grattarola, D., Alippi, C.: Spectral clustering with graph neural networks for graph pooling. In: International Conference on Machine Learning, pp. 874–883 (2020). PMLR
Dong, X., Huang, J., Qin, F., Xudong, H.: Graph pooling method based on multilevel union. J. Beijing Univ. Aeronaut. Astronaut. (2022)
Du, J., Wang, S., Miao, H., Zhang, J.: Multi-channel pooling graph neural networks. In: IJCAI, pp. 1442–1448 (2021)
Yanardag, P., Vishwanathan, S.: Deep graph kernels. In: Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1365–1374 (2015)
Dobson, P.D., Doig, A.J.: Distinguishing enzyme structures from non-enzymes without alignments. J. Mol. Biol. 330(4), 771–783 (2003)
Kazius, J., McGuire, R., Bursi, R.: Derivation and validation of toxicophores for mutagenicity prediction. J. Med. Chem. 48(1), 312–320 (2005)
Ranjan, E., Sanyal, S., Talukdar, P.: Asap: Adaptive structure aware pooling for learning hierarchical graph representations. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 34, pp. 5470–5477 (2020)
Pang, Y., Zhao, Y., Li, D.: Graph pooling via coarsened graph infomax. In: Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 2177–2181 (2021)
Baek, J., Kang, M., Hwang, S.J.: Accurate learning of graph representations with graph multiset pooling. arXiv preprint arXiv:2102.11533 (2021)
Zhou, X., Yin, J., Tsang, I.W.: Edge but not least: Cross-view graph pooling. arXiv preprint arXiv:2109.11796 (2021)
Wu, J., Chen, X., Xu, K., Li, S.: Structural entropy guided graph hierarchical pooling. In: International Conference on Machine Learning, pp. 24017–24030 (2022). PMLR
Zhang, M., Cui, Z., Neumann, M., Chen, Y.: An end-to-end deep learning architecture for graph classification. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32 (2018)
Acknowledgements
This work is supported by the Natural Science Foundation of China: 61806005, the University Synergy Innovation Program of Anhui Province: GXXT-2022-052 and GXXT-2020-012, the Outstanding Young Talents Support Program of Anhui Province: gxyqZD2022032, and the Natural Science Foundation of the Educational Commission of Anhui Province of China: KJ2021A0373.
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Yuanyuan Wang constructed the model and experiments, Jun Huang wrote the main manuscript. All authors reviewed the manuscript.
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Huang, J., Wang, YY. Multi-view parallel graph pooling. Int J Data Sci Anal (2023). https://doi.org/10.1007/s41060-023-00476-8
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DOI: https://doi.org/10.1007/s41060-023-00476-8