Skip to main content

Pessimistic Adversarially Regularized Learning for Graph Embedding

  • Conference paper
  • First Online:
Advanced Data Mining and Applications (ADMA 2023)

Abstract

Autoencoder frameworks have been effectively employed for graph embedding, resulting in successful analysis of graph in low-dimensional space. Recently, generative models (GANs), which learn data distribution of the adversarial method have been increasingly applied to graph autoencoders (GAEs). Despite the effectiveness of current research, many GAEs lack the ability to provide instantaneous feedback and ensure stable updates within the GAN component. In particular, the MiniMax Multi-Agent Deep Deterministic Policy Gradient (M3DDPG) has demonstrated that using a 1-step gradient descent can enhance the performance, which can also be leveraged to train the encoder to further improve the adaptability of graph embedding. Motivated by this, we propose the Pessimistic Graph Autoencoder (PGAE), and its variational version Pessimistic Variational Graph Autoencoder (PVGAE). These methods reduce the output probability of the discriminator module through pessimistic parameters which make the feature distribution generated by encoder restore maximally the actual distribution of the original graph. Furthermore, we employ graph embedding to reconstruct the original graph information and constrain the generation of embedding vectors to preserve topological structure and node content of the original graph. Our approaches yield competitive results in node clustering and node classification tasks, outperforming numerous state-of-the-art graph autoencoders across three benchmark datasets.

M. Li and Y. Song—Equal contribution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Xu, M.: Understanding graph embedding methods and their applications. SIAM Rev. 63(4), 825–853 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cai, H., Zheng, V.W., Chang, K.C.C.: A comprehensive survey of graph embedding: problems, techniques, and applications. IEEE Trans. Knowl. Data Eng. 30(9), 1616–1637 (2018)

    Article  Google Scholar 

  3. Cui, P., Wang, X., Pei, J., Zhu, W.: A survey on network embedding. IEEE Trans. Knowl. Data Eng. 31(5), 833–852 (2018)

    Article  Google Scholar 

  4. Ou, M., Cui, P., Pei, J., Zhang, Z., Zhu, W.: Asymmetric transitivity preserving graph embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1105–1114 (2016)

    Google Scholar 

  5. Grover, A., Leskovec, J.: node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 855–864 (2016)

    Google Scholar 

  6. Qiu, J., Dong, Y., Ma, H., Li, J., Wang, K., Tang, J.: Network embedding as matrix factorization: unifying DeepWalk, LINE, PTE, and node2vec. In: Proceedings of the Eleventh ACM International Conference on Web Search and Data Mining, pp. 459–467 (2018)

    Google Scholar 

  7. He, D., et al.: Adversarial mutual information learning for network embedding. In: IJCAI, pp. 3321–3327 (2020)

    Google Scholar 

  8. Scarselli, F., Gori, M., Tsoi, A.C., Hagenbuchner, M., Monfardini, G.: The graph neural network model. IEEE Trans. Neural Networks 20(1), 61–80 (2008)

    Article  Google Scholar 

  9. Kipf, T.N., Welling, M.: Variational graph auto-encoders. arXiv preprint arXiv:1611.07308 (2016)

  10. Wang, C., Pan, S., Long, G., Zhu, X., Jiang, J.: MGAE: marginalized graph autoencoder for graph clustering. In: Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, pp. 889–898 (2017)

    Google Scholar 

  11. Park, J., Lee, M., Chang, H.J., Lee, K., Choi, J.Y.: Symmetric graph convolutional autoencoder for unsupervised graph representation learning. In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 6519–6528 (2019)

    Google Scholar 

  12. Goodfellow, I., et al.: Generative adversarial networks. Commun. ACM 63(11), 139–144 (2020)

    Article  MathSciNet  Google Scholar 

  13. Zheng, S., Zhu, Z., Zhang, X., Liu, Z., Cheng, J., Zhao, Y.: Distribution-induced bidirectional generative adversarial network for graph representation learning. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 7224–7233 (2020)

    Google Scholar 

  14. Liang, H., Gao, J.: Wasserstein adversarially regularized graph autoencoder. arXiv preprint arXiv:2111.04981 (2021)

  15. Li, S., Wu, Y., Cui, X., Dong, H., Fang, F., Russell, S.: Robust multi-agent reinforcement learning via minimax deep deterministic policy gradient. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 4213–4220 (2019)

    Google Scholar 

  16. Ahmed, A., Shervashidze, N., Narayanamurthy, S., Josifovski, V., Smola, A.J.: Distributed large-scale natural graph factorization. In: Proceedings of the 22nd International Conference on World Wide Web, pp. 37–48 (2013)

    Google Scholar 

  17. Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., Philip, S.Y.: A comprehensive survey on graph neural networks. IEEE Trans. Neural Netw. Learn. Syst. 32(1), 4–24 (2020)

    Article  MathSciNet  Google Scholar 

  18. Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., Bengio, Y.: Graph attention networks. arXiv preprint arXiv:1710.10903 (2017)

  19. Hamilton, W., Ying, Z., Leskovec, J.: Inductive representation learning on large graphs. In: Advances in Neural Information Processing Systems, vol. 30 (2017)

    Google Scholar 

  20. Dai, H., Kozareva, Z., Dai, B., Smola, A., Song, L.: Learning steady-states of iterative algorithms over graphs. In: International Conference on Machine Learning, pp. 1106–1114. PMLR (2018)

    Google Scholar 

  21. Atwood, J., Towsley, D.: Diffusion-convolutional neural networks. In: Advances in Neural Information Processing Systems, vol. 29 (2016)

    Google Scholar 

  22. Tu, K., Cui, P., Wang, X., Yu, P.S., Zhu, W.: Deep recursive network embedding with regular equivalence. In: Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2357–2366 (2018)

    Google Scholar 

  23. Li, Y., Yu, R., Shahabi, C., Liu, Y.: Diffusion convolutional recurrent neural network: data-driven traffic forecasting. arXiv preprint arXiv:1707.01926 (2017)

  24. Tian, F., Gao, B., Cui, Q., Chen, E., Liu, T.Y.: Learning deep representations for graph clustering. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 28 (2014)

    Google Scholar 

  25. Wang, D., Cui, P., Zhu, W.: Structural deep network embedding. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1225–1234 (2016)

    Google Scholar 

  26. Kingma, D.P., Welling, M.: Auto-encoding variational Bayes. arXiv preprint arXiv:1312.6114 (2013)

  27. Pan, S., Hu, R., Long, G., Jiang, J., Yao, L., Zhang, C.: Adversarially regularized graph autoencoder for graph embedding. arXiv preprint arXiv:1802.04407 (2018)

  28. Liu, X., Du, H., Xu, J., Qiu, B.: DBGAN: a dual-branch generative adversarial network for undersampled MRI reconstruction. Magn. Reson. Imaging 89, 77–91 (2022)

    Article  Google Scholar 

  29. Goldberger, J., Gordon, S., Greenspan, H., et al.: An efficient image similarity measure based on approximations of KL-divergence between two Gaussian mixtures. In: ICCV, vol. 3, pp. 487–493 (2003)

    Google Scholar 

  30. Guo, L., Dai, Q.: Graph clustering via variational graph embedding. Pattern Recogn. 122, 108334 (2022)

    Article  Google Scholar 

  31. Wattenberg, M., Viégas, F., Johnson, I.: How to use t-SNE effectively. Distill 1(10), e2 (2016)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gongju Wang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Li, M. et al. (2023). Pessimistic Adversarially Regularized Learning for Graph Embedding. In: Yang, X., et al. Advanced Data Mining and Applications. ADMA 2023. Lecture Notes in Computer Science(), vol 14178. Springer, Cham. https://doi.org/10.1007/978-3-031-46671-7_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-46671-7_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-46670-0

  • Online ISBN: 978-3-031-46671-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics