Abstract
The node drop pooling is a significant type of graph pooling that is required for learning graph-level representations. However, existing node drop pooling models still suffer from the information loss problem, impairing their effectiveness in graph classification. To mitigate the detrimental effect of the information loss, we propose a novel and flexible technique called Masked Graph Auto-encoder constrained Pooling (MGAP), which enables vanilla node drop pooling methods to retain sufficient effective graph information from both node-attribute and network-topology perspectives. Specifically, MGAP reconstructs the original node attributes of the graph using a graph convolutional network and the node degree of the graph (i.e., structural information) using a feedforward neural network with exponential neurons from the pooled (masked) graphs generated by the vanilla node drop pooling models. Notably, MGAP is a plug-and-play technique that can be directly adopted in the current node drop pooling methods. To evaluate the effectiveness of MGAP, we conduct extensive experiments on eleven real-world datasets by applying MGAP to three commonly-used methods, i.e., TopKPool, SAGPool, and GSAPool. The experimental results reveal that MGAP has the capacity to consistently improve the performance of all the three node drop pooling models in the graph classification task.
C. Liu—This work has been done when Chuang Liu was an intern at JD Explore Academy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In some very specific cases, there exists \( |\mathcal {V}^{\prime }| \ge |\mathcal {V}| \), causing the graph to be up scaled by pooling.
- 2.
The source code is available at https://github.com/liucoo/mgap.
References
Baek, J., Kang, M., Hwang, S.J.: Accurate learning of graph representations with graph multiset pooling. In: ICLR (2021)
Bai, L., Jiao, Y., Cui, L., Hancock, E.R.: Learning aligned-spatial graph convolutional networks for graph classification. In: ECML-PKDD, pp. 464–482 (2019)
Bianchi, F.M., Grattarola, D., Alippi, C.: Spectral clustering with graph neural networks for graph pooling. In: ICML. vol. 119, pp. 874–883 (2020)
Cai, C., Wang, D., Wang, Y.: Graph coarsening with neural networks. In: ICLR (2021)
Duvenaud, D., et al.: Convolutional networks on graphs for learning molecular fingerprints. In: NeurIPS, pp. 2224–2232 (2015)
Errica, F., Podda, M., Bacciu, D., Micheli, A.: A fair comparison of graph neural networks for graph classification. In: ICLR (2020)
Gao, H., Ji, S.: Graph u-nets. In: ICML, pp. 2083–2092 (2019)
Gao, X., Dai, W., Li, C., Xiong, H., Frossard, P.: ipool-information-based pooling in hierarchical graph neural networks. IEEE Trans. Neural Netw. Learn. Syst. 33(9), 5032–5044 (2021)
Grattarola, D., Zambon, D., Bianchi, F.M., Alippi, C.: Understanding pooling in graph neural networks. arXiv:2110.05292 (2021)
Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. In: NeurIPS, vol. 30 (2017)
Kingma, D.P., Ba, J.: Adam: A method for stochastic optimization. arXiv:1412.6980 (2014)
Kipf, T.N., Welling, M.: Variational graph auto-encoders. In: NeurIPS Workshop on Bayesian Deep Learning (2016)
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)
Li, J., Li, J., Liu, Y., Yu, J., Li, Y., Cheng, H.: Deconvolutional networks on graph data. In: NeurIPS (2021)
Li, M., Chen, S., Zhang, Y., Tsang, I.: Graph cross networks with vertex infomax pooling. In: NeurIPS, vol. 33, pp. 14093–14105 (2020)
Li, X., et al.: Braingnn: Interpretable brain graph neural network for fmri analysis. Med. Image Anal. 73, 102233 (2021)
Li, X., Zhang, H., Zhang, R.: Adaptive graph auto-encoder for general data clustering. IEEE Trans. Patt. Anal. Mach. Intell. 44(12), 9725–9732 (2021)
Liu, C., Zhan, Y., Li, C., Du, B., Wu, J., Hu, W., Liu, T., Tao, D.: Graph pooling for graph neural networks: Progress, challenges, and opportunities. arXiv:2204.07321 (2022)
Ma, Y., Wang, S., Aggarwal, C.C., Tang, J.: Graph convolutional networks with eigenpooling. In: SIGKDD, pp. 723–731 (2019)
Mathieu, E., Le Lan, C., Maddison, C.J., Tomioka, R., Teh, Y.W.: Continuous hierarchical representations with poincaré variational auto-encoders. In: NeurIPS (2019)
McPherson, M., Smith-Lovin, L., Cook, J.M.: Birds of a feather: Homophily in social networks. Ann. Rev. sociol. 27(1), 415–444 (2001)
Mesquita, D., Souza, A., Kaski, S.: Rethinking pooling in graph neural networks. In: NeurIPS. vol. 33, pp. 2220–2231 (2020)
Park, J., Cho, J., Chang, H.J., Choi, J.Y.: Unsupervised hyperbolic representation learning via message passing auto-encoders. In: CVPR, pp. 5516–5526 (2021)
Park, J., Lee, M., Chang, H.J., Lee, K., Choi, J.Y.: Symmetric graph convolutional autoencoder for unsupervised graph representation learning. In: ICCV, pp. 6519–6528 (2019)
Rhee, S., Seo, S., Kim, S.: Hybrid approach of relation network and localized graph convolutional filtering for breast cancer subtype classification. In: IJCAI, pp. 3527–3534 (2018)
Salha, G., Hennequin, R., Remy, J.B., Moussallam, M., Vazirgiannis, M.: Fastgae: scalable graph autoencoders with stochastic subgraph decoding. Neural Netw. 142, 1–19 (2021)
Salha, G., Hennequin, R., Tran, V.A., Vazirgiannis, M.: A degeneracy framework for scalable graph autoencoders. In: IJCAI, pp. 3353–3359 (2019)
Salha, G., Hennequin, R., Vazirgiannis, M.: Simple and effective graph autoencoders with one-hop linear models. In: ECML-PKDD, pp. 319–334 (2020)
Salha, G., Limnios, S., Hennequin, R., Tran, V.A., Vazirgiannis, M.: Gravity-inspired graph autoencoders for directed link prediction. In: CIKM, pp. 589–598 (2019)
Sun, D., Li, D., Ding, Z., Zhang, X., Tang, J.: Dual-decoder graph autoencoder for unsupervised graph representation learning. Knowl.-Based Syst. 234, 107564 (2021)
Tang, M., Li, P., Yang, C.: Graph auto-encoder via neighborhood wasserstein reconstruction. In: ICLR (2022)
Veličković, P., Cucurull, G., Casanova, A., Romero, A., Liò, P., Bengio, Y.: Graph attention networks. In: ICLR (2018)
Wang, Z., Ji, S.: Second-order pooling for graph neural networks. IEEE Trans. Pattern Anal. Mach. Intell. (2020, early access). https://doi.org/10.1109/TPAMI.2020.2999032
Winter, R., Noé, F., Clevert, D.A.: Permutation-invariant variational autoencoder for graph-level representation learning. In: NeurIPS, vol. 34 (2021)
Xu, K., Hu, W., Leskovec, J., Jegelka, S.: How powerful are graph neural networks? In: ICLR (2019)
Ying, Z., You, J., Morris, C., Ren, X., Hamilton, W., Leskovec, J.: Hierarchical graph representation learning with differentiable pooling. In: NeurIPS. pp. 4805–4815 (2018)
Yuan, H., Ji, S.: Structpool: Structured graph pooling via conditional random fields. In: ICLR (2020)
Zhang, L., et al.: Structure-feature based graph self-adaptive pooling. In: WWW, pp. 3098–3104 (2020)
Zhang, M., Cui, Z., Neumann, M., Chen, Y.: An end-to-end deep learning architecture for graph classification. In: AAAI (2018)
Zhang, Z., et al.: Hierarchical multi-view graph pooling with structure learning. IEEE Trans. Knowl. Data Eng. 34(1), 545–559 (2021)
Acknowledgements
This work was supported in part by the Natural Science Foundation of China (Nos. 61976162, 82174230, 62002090), Artificial Intelligence Innovation Project of Wuhan Science and Technology Bureau (No.2022010702040070), Science and Technology Major Project of Hubei Province (Next Generation AI Technologies) (No. 2019AEA170), and Joint Fund for Translational Medicine and Interdisciplinary Research of Zhongnan Hospital of Wuhan University (No. ZNJC202016).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Liu, C., Zhan, Y., Ma, X., Tao, D., Du, B., Hu, W. (2023). Masked Graph Auto-Encoder Constrained 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_23
Download citation
DOI: https://doi.org/10.1007/978-3-031-26390-3_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-26389-7
Online ISBN: 978-3-031-26390-3
eBook Packages: Computer ScienceComputer Science (R0)
