[go: up one dir, main page]
Skip to main content
SpringerLink
Log in

MST-HGCN: a minimum spanning tree hyperbolic graph convolutional network

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Graph neural networks (GNNs) have achieved outstanding results in research tasks on graph data. Most existing GNN models are defined in Euclidean space. However, when embedding hierarchical and scale-free graphs, models lying in hyperbolic space attain significant improvements over Euclidean graph convolutional networks (GCNs). To further enhance the performance of hyperbolic graph convolution and expand the applicability of related models to different data, we propose a hyperbolic graph convolution model based on the minimum spanning tree (MST-HGCN). Our method utilizes the minimum spanning tree (MST) algorithm to extract and process the topological structure of the input graph, which yields a more hierarchical topological structure and largely eliminates noisy edges. Then, several different topological structures based on the same spanning tree are produced by randomly re-adding the edges deleted by the MST algorithm; subsequently, a consistency loss is introduced to jointly optimize different outputs obtained from these topological structures. Experiments on node classification tasks and link prediction tasks for datasets with different hierarchy extents show that, our method comprehensively outperforms the vanilla hyperbolic GCN model on all the datasets, approaching or even outperforming the representative Euclidean comparison methods, which indicates that our method has better performance and data applicability.

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

Access this article

Log in via an institution

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

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Algorithm 1
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data Availability

The datasets analysed during the current study are available in the HGCN repository, https://github.com/HazyResearch/hypgcn.

Notes

  1. https://github.com/dmlc/dgl

  2. https://github.com/optuna/optuna

References

  1. Kipf TN, Welling M (2017) Semi-supervised classification with graph convolutional networks. In: 5th International conference on learning representations, ICLR, Toulon, France, 24-26 April 2017, conference track proceedings

  2. Chami I, Ying Z, Ré C, Leskovec J (2019) Hyperbolic graph convolutional neural networks. In: Wallach H, Larochelle H, Beygelzimer A, Dalché-buc F, Fox E, Garnett R (eds) Advances in neural information processing systems

  3. Rong Y, Huang W, Xu T, Huang J (2019) Dropedge: towards deep graph convolutional networks on node classification. In: International conference on learning representations

  4. Chen H, Xu Y, Huang F, Deng Z, Huang W, Wang S, He P, Li Z (2020) Label-aware graph convolutional networks. In: Proceedings of the 29th ACM international conference on information & knowledge management. ACM, pp 1977–1980. https://doi.org/10.1145/3340531.3412139

  5. Corso G, Cavalleri L, Beaini D, Liò P, Veličković P (2020) Principal neighbourhood aggregation for graph nets. In: Advances in neural information processing systems, vol 33, pp 13260–13271

  6. Jonckheere E, Lohsoonthorn P, Bonahon F (2008) Scaled gromov hyperbolic graphs. J Graph Theory 57(2):157–180. https://doi.org/10.1002/jgt.20275

    Article  MathSciNet  MATH  Google Scholar 

  7. Feng W, Zhang J, Dong Y, Han Y, Luan H, Xu Q, Yang Q, Kharlamov E, Tang J (2020) Graph random neural networks for semi-supervised learning on graphs. In: Proceedings of the 34th international conference on neural information processing systems. NIPS’20. Curran associates inc., pp 22092–22103

  8. Xie Q, Dai Z, Hovy E, Luong T, Le Q (2020) Unsupervised data augmentation for consistency training. In: Advances in neural information processing systems, vol 33, pp 6256–6268

  9. Gori M, Monfardini G, Scarselli F (2005) A new model for learning in graph domains. In: Proceedings. 2005 IEEE international joint conference on neural networks. IEEE, vol 2, pp 729–734. https://doi.org/10.1109/IJCNN.2005.1555942

  10. Scarselli F, Gori M, Ah Chung Tsoi, Hagenbuchner M, Monfardini G (2009) The graph neural network model. IEEE Trans Neural Netw 20(1):61–80. https://doi.org/10.1109/TNN.2008.2005605https://doi.org/10.1109/TNN.2008.2005605

    Article  Google Scholar 

  11. Perozzi B, Al-Rfou R, Skiena S (2014) Deepwalk: online learning of social representations. In: Proceedings of the 20th ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 701–710. https://doi.org/10.1145/2623330.2623732https://doi.org/10.1145/2623330.2623732

  12. Grover A, Leskovec J (2016) Node2vec: scalable feature learning for networks. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 855–864. https://doi.org/10.1145/2939672.2939754

  13. Tang J, Qu M, Wang M, Zhang M, Yan J, Mei Q (2015) LINE: large-scale information network embedding. In: Proceedings of the 24th international conference on world wide web. International world wide web conferences steering committee, pp 1067–1077. https://doi.org/10.1145/2736277.2741093

  14. Qiu J, Dong Y, Ma H, Li J, Wang K, Tang J (2018) 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. ACM, pp 459–467. https://doi.org/10.1145/3159652.3159706

  15. Zhang J, Dong Y, Wang Y, Tang J, Ding M (2019) ProNE: fast and scalable network representation learning. In: IJCAI. 2019, 19: 4278-4284, vol 19, pp 4278–4284

  16. Cao S, Lu W, Xu Q (2015) Grarep: learning graph representations with global structural information. In: Proceedings of the 24th ACM international on conference on information and knowledge management. ACM, pp 891–900. https://doi.org/10.1145/2806416.2806512

  17. Ou M, Cui P, Pei J, Zhang Z, Zhu W (2016) Asymmetric transitivity preserving graph embedding. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining. ACM, pp 1105–1114. https://doi.org/10.1145/2939672.2939751

  18. Defferrard M, Bresson X, Vandergheynst P (2016) Convolutional neural networks on graphs with fast localized spectral filtering. In: Advances in neural information processing systems, vol 29

  19. Chen J, Ma T, Xiao C (2018) FastGCN: fast learning with graph convolutional networks via importance sampling. In: International conference on learning representations

  20. Wu F, Souza A, Zhang T, Fifty C, Yu T, Weinberger K (2019) Simplifying graph convolutional networks. In: International conference on machine learning. PMLR, 6861–6871

  21. Huang W, Zhang T, Rong Y, Huang J (2018) Adaptive sampling towards fast graph representation learning. In: Proceedings of the 32nd international conference on neural information processing systems. NIPS’18. Curran associates inc., pp 4563–4572

  22. Veličković P, Cucurull G, Casanova A, Romero A, Liò P, Bengio Y (2018) Graph attention networks. In: International conference on learning representations

  23. Xu K, Hu W, Leskovec J, Jegelka S (2019) How powerful are graph neural networks?. In: International conference on learning representations

  24. Hamilton WL, Ying R, Leskovec J (2017) Inductive representation learning on large graphs. In: Proceedings of the 31st international conference on neural information processing systems. NIPS’17. Curran associates inc., pp 1025–1035

  25. Schlichtkrull M, Kipf TN, Bloem P, Van Den Berg R, Titov I, Welling M (2018) Modeling relational data with graph convolutional networks. In: Gangemi A, Navigli R, Vidal M-E, Hitzler P, Troncy R, Hollink L, Tordai A, Alam M (eds) The semantic web. Lecture notes in computer science. Springer international publishing, pp 593–607. https://doi.org/10.1007/978-3-319-93417-4_38

  26. Bruna J, Zaremba W, Szlam A, LeCun Y (2014) Spectral networks and deep locally connected networks on graphs. In: 2nd International conference on learning representations, ICLR 2014

  27. Henaff M, Bruna J, Lecun Y (2015) Deep convolutional networks on graph-structured data

  28. Monti F, Boscaini D, Masci J, Rodola E, Svoboda J, Bronstein MM (2017) Geometric deep learning on graphs and manifolds using mixture model CNNs. In: 2017 IEEE conference on computer vision and pattern recognition (CVPR). IEEE, pp 5425–5434. https://doi.org/10.1109/CVPR.2017.576

  29. Nt H, Maehara T, Murata T (2021) Revisiting graph neural networks: graph filtering perspective. In: 2020 25Th international conference on pattern recognition (ICPR). IEEE, Milan, Italy, pp 8376–8383. https://doi.org/10.1109/ICPR48806.2021.9412278

  30. Gilmer J, Schoenholz SS, Riley PF, Vinyals O, Dahl GE (2017) Neural message passing for quantum chemistry. In: Proceedings of the 34th international conference on machine learning - vol 70. ICML’17. JMLR.org, pp 1263–1272

  31. Liang Y, Meng F, Zhang Y, Chen Y, Xu J, Zhou J (2022) Emotional conversation generation with heterogeneous graph neural network. Artif Intell 308:103714. https://doi.org/10.1016/j.artint.2022.103714https://doi.org/10.1016/j.artint.2022.103714

    Article  Google Scholar 

  32. Fu X, Qi Q, Zha Z-J, Ding X, Wu F, Paisley J (2021) Successive graph convolutional network for image de-raining. Int J Comput Vis 129(5):1691–1711. https://doi.org/10.1007/s11263-020-01428-6https://doi.org/10.1007/s11263-020-01428-6

    Article  Google Scholar 

  33. Dhingra B, Shallue C, Norouzi M, Dai A, Dahl G (2018) Embedding text in hyperbolic spaces. In: Proceedings of the twelfth workshop on graph-based methods for natural language processing (TextGraphs-12). Association for computational linguistics, pp 59–69. https://doi.org/10.18653/v1/W18-1708

  34. Tay Y, Tuan LA, Hui SC (2018) Hyperbolic representation learning for fast and efficient neural question answering. In: Proceedings of the eleventh ACM international conference on web search and data mining. ACM, pp 583–591. https://doi.org/10.1145/3159652.3159664https://doi.org/10.1145/3159652.3159664

  35. Khrulkov V, Mirvakhabova L, Ustinova E, Oseledets I, Lempitsky V (2020) Hyperbolic image embeddings. In: 2020 IEEE/CVF conference on computer vision and pattern recognition (CVPR). IEEE, pp 6417–6427. https://doi.org/10.1109/CVPR42600.2020.00645https://doi.org/10.1109/CVPR42600.2020.00645

  36. Ganea O, Bécigneul G, Hofmann T (2018) Hyperbolic neural networks. In: Proceedings of the 32nd international conference on neural information processing systems, vol 31, pp 5350–5360

  37. Gulcehre C, Denil M, Malinowski M, Razavi A, Pascanu R, Hermann KM, Battaglia P, Bapst V, Raposo D, Santoro A, de Freitas N (2018) Hyperbolic attention networks. In: International conference on learning representations

  38. Chamberlain BP, Clough JR, Deisenroth MP (2017) Neural embeddings of graphs in hyperbolic space. CoRR. MLG Workshop 2017

  39. Liu Q, Nickel M, Kiela D (2019) Hyperbolic graph neural networks. In: Advances in neural information processing systems, vol 32

  40. Sun L, Zhang Z, Zhang J, Wang F, Peng H, Su S, Yu PS (2021) Hyperbolic variational graph neural network for modeling dynamic graphs. Proc AAAI Conf Artif intell 35(5):4375–4383

    Google Scholar 

  41. Sun Z, Chen M, Hu W, Wang C, Dai J, Zhang W (2020) Knowledge association with hyperbolic knowledge graph embeddings. In: Proceedings of the 2020 conference on empirical methods in natural language processing (EMNLP). Association for computational linguistics, pp 5704–5716. https://doi.org/10.18653/v1/2020.emnlp-main.460https://doi.org/10.18653/v1/2020.emnlp-main.460

  42. Zhang Y, Wang X, Shi C, Jiang X, Ye YF (2021) Hyperbolic graph attention network. IEEE Trans Big Data:1–1. https://doi.org/10.1109/TBDATA.2021.3081431https://doi.org/10.1109/TBDATA.2021.3081431

  43. Liu J, Yang M, Zhou M, Feng S, Fournier-Viger P (2022) Enhancing hyperbolic graph embeddings via contrastive learning. In: NeurIPS’21@2nd workshop on self-supervised learning. 35th conference on neural information processing systems (neurIPS 2021)

  44. Dai J, Wu Y, Gao Z, Jia Y (2021) A hyperbolic-to-hyperbolic graph convolutional network. In: 2021 IEEE/CVF conference on computer vision and pattern recognition (CVPR). IEEE, pp 154–163. https://doi.org/10.1109/CVPR46437.2021.00022

  45. Nickel M, Kiela D (2017) Poincaré embeddings for learning hierarchical representations. In: Advances in neural information processing systems, vol 30

  46. Berthelot D, Carlini N, Goodfellow I, Papernot N, Oliver A, Raffel CA (2019) Mixmatch: a holistic approach to semi-supervised learning. In: Advances in neural information processing systems, vol 32

  47. Leskovec J, Sosič R (2016) SNAP: a general-purpose network analysis and graph-mining library. ACM Trans Intell Syst Technol 8(1):1–20. https://doi.org/10.1145/2898361

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Beihang University, XueYuan Road No.37, Beijing, 100191, Beijing, China

    Yanxi Liu, Bo Lang & Fengnan Quan

Authors
  1. Yanxi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Lang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fengnan Quan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanxi Liu.

Ethics declarations

Conflict of Interests

We declare that we have no financial or personal relationships with other people or organizations that can inappropriately influence our work.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Lang, B. & Quan, F. MST-HGCN: a minimum spanning tree hyperbolic graph convolutional network. Appl Intell 53, 14515–14526 (2023). https://doi.org/10.1007/s10489-022-04256-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-022-04256-y

Keywords

Search

Navigation