Skip to main content

Advertisement

Springer Nature Link
Log in

SLRNode: node similarity-based leading relationship representation layer in graph neural networks for node classification

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

For semi-supervised node classification in graph neural network models (GNNs), the representativeness of pseudo-labeled nodes greatly influences the ultimate performance. Most existing studies fail to consider the partial order relationship between nodes, leading to the generated pseudo-labels not necessarily being representative. This paper proposes a method for constructing a leading tree on graph data to select center nodes. This method integrates the leading tree structure into the GNN and introduces a node similarity-based leading relationship representation layer, which can select the most critical subset of nodes in the graph. These nodes’ pseudo-labels are inferred in a self-supervised manner and added to the node label set for training. Additionally, due to the advantages of the leading tree structure, the number of noisy labels is significantly reduced, greatly alleviating the negative impact of noisy labels on model training. This paper also designs a dual-model pseudo-label training framework, where one model generates pseudo-labels by incorporating leading trees, and the other model is used to predict node labels. Node classification experiments were conducted on six datasets to show the advantages of the proposed architecture.

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
Algorithm 1
Fig. 2
Algorithm 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

We have shared the link to our data in the paper.

References

  1. Zou M, Gan Z, Cao R, Guan C, Leng S (2023) Similarity-navigated graph neural networks for node classification. Inf Sci 633:41–69. https://doi.org/10.1016/j.ins.2023.03.057

    Article  MATH  Google Scholar 

  2. Mvula PK, Branco P, Jourdan G-V, Viktor HL (2024) A survey on the applications of semi-supervised learning to cyber-security. ACM Comput Surv 56(10):1–41. https://doi.org/10.1145/3657647

    Article  MATH  Google Scholar 

  3. Wang Z, Ding H, Pan L, Li J, Gong Z, Yu PS (2024) From cluster assumption to graph convolution: graph-based semi-supervised learning revisited. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2024.3454710

    Article  MATH  Google Scholar 

  4. Huang C, Wang J, Wang S, Zhang Y (2023) A review of deep learning in dentistry. Neurocomputing. https://doi.org/10.1016/j.neucom.2023.126629

    Article  MATH  Google Scholar 

  5. Peng M, Juan X, Li Z (2024) Label-guided graph contrastive learning for semi-supervised node classification. Expert Syst Appl 239:122385–122398. https://doi.org/10.1016/j.eswa.2023.122385

    Article  MATH  Google Scholar 

  6. Zhou Z-H (2021) Semi-supervised learning. Mach Learn. https://doi.org/10.1007/978-981-15-1967-3_13

    Article  MATH  Google Scholar 

  7. Duarte JM, Berton L (2023) A review of semi-supervised learning for text classification. Artif Intell Rev 56(9):9401–9469. https://doi.org/10.1007/s10462-023-10393-8

    Article  MATH  Google Scholar 

  8. Daneshfar F, Soleymanbaigi S, Yamini P, Amini MS (2024) A survey on semi-supervised graph clustering. Eng Appl Artif Intell 133:108215–108251. https://doi.org/10.1016/j.engappai.2024.108215

    Article  Google Scholar 

  9. Yue C, Jha NK (2024) Ctrl: clustering training losses for label error detection. IEEE Trans Artif Intell. https://doi.org/10.1109/TAI.2024.3365093

    Article  MATH  Google Scholar 

  10. Ouyang J, Mao D, Meng Q (2024) Larw: boosting open-set semi-supervised learning with label-guided re-weighting. Multimedia Tools Appl 83(15):46419–46437. https://doi.org/10.1007/s11042-023-17357-8

    Article  Google Scholar 

  11. Yang Y, Jiang N, Xu Y, Zhan D-C (2024) Robust semi-supervised learning by wisely leveraging open-set data. IEEE Trans Pattern Anal Mach Intell. https://doi.org/10.1109/TPAMI.2024.3403994

    Article  MATH  Google Scholar 

  12. Li K, Ye W (2022) Semi-supervised node classification via graph learning convolutional neural network. Appl Intell 52(11):12724–12736. https://doi.org/10.1007/s10489-022-03233-9

    Article  MATH  Google Scholar 

  13. Sun H, Li X, Wu Z, Su D, Li R-H, Wang G (2024) Breaking the entanglement of homophily and heterophily in semi-supervised node classification. In: 2024 IEEE 40th International Conference on Data Engineering (ICDE). IEEE, pp 2379–2392. https://doi.org/10.1109/ICDE60146.2024.00188

  14. Wu L, Cui P, Pei J, Zhao L, Guo X (2022) Graph neural networks: foundation, frontiers and applications. In: Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp 4840–4841. https://doi.org/10.1145/3534678.3542609

  15. Shen G, Zeng W, Yang J (2024) Research on migraine classification model based on hypergraph neural network. J Supercomput 80(17):25403–25423. https://doi.org/10.1007/s11227-024-06387-0

    Article  MATH  Google Scholar 

  16. Sharma K, Lee Y-C, Nambi S, Salian A, Shah S, Kim S-W, Kumar S (2024) A survey of graph neural networks for social recommender systems. ACM Comput Surv 56(10):1–34. https://doi.org/10.1145/3661821

    Article  MATH  Google Scholar 

  17. Wang Y, Li Z, Farimani AB (2023) Graph neural networks for molecules. Mach Learn Mol Sci. https://doi.org/10.1007/978-3-031-37196-7_2

    Article  MATH  Google Scholar 

  18. Yao C, Huang H, Gao H, Wu F, Chen H, Zhao J (2024) Molecular graph representation learning via structural similarity information. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases. Springer, pp 351–367. https://doi.org/10.1007/978-3-031-70352-2_21

  19. 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 Computer Society, pp 5425–5434. https://doi.org/10.48550/arXiv.1611.08402

  20. 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, pp 1025–1035

  21. Veličković P, Cucurull G, Casanova A, Romero A, Liò P, Bengio Y (2018) Graph attention networks. In: International Conference on Learning Representations, pp 1–12. https://doi.org/10.48550/arXiv.1710.10903

  22. Xiao Y, Xu J, Yang J, Li S, Wang G (2025) Determinate node selection for semi-supervised classification oriented graph convolutional networks. Int J Bio-Inspired Comput. https://doi.org/10.1504/IJBIC.2025.143648

    Article  MATH  Google Scholar 

  23. Wei X, Gong X, Zhan Y, Du B, Luo Y, Hu W (2023) Clnode: curriculum learning for node classification. In: Proceedings of the Sixteenth ACM International Conference on Web Search and Data Mining, pp 670–678. https://doi.org/10.1145/3539597.3570385

  24. Nguyen T-T, Nguyen P, Luu K (2024) Hig: hierarchical interlacement graph approach to scene graph generation in video understanding. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp 18384–18394. https://doi.org/10.48550/arXiv.2312.03050

  25. Gui Q, Zhou H, Guo N, Niu B (2023) A survey of class-imbalanced semi-supervised learning. Mach Learn. https://doi.org/10.1007/s10994-023-06344-7

    Article  MATH  Google Scholar 

  26. Ojaghi B, Dehshibi MM, Antonopoulos A (2024) A supervised active learning method for identifying critical nodes in iot networks. J Supercomput. https://doi.org/10.1007/s11227-024-06103-y

    Article  MATH  Google Scholar 

  27. Lazarow J, Sohn K, Lee C-Y, Li C-L, Zhang Z, Pfister T (2023) Unifying distribution alignment as a loss for imbalanced semi-supervised learning. In: Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pp 5644–5653. https://doi.org/10.1109/WACV56688.2023.00560

  28. Ma R, Gao J, Cheng L, Zhang Y, Petrosian O (2024) Dagcn: hybrid model for efficiently handling joint node and link prediction in cloud workflows. Appl Intell 54(23):12505–12530. https://doi.org/10.1007/s10489-024-05828-w

    Article  Google Scholar 

  29. Sun C, Li C, Lin X, Zheng T, Meng F, Rui X, Wang Z (2023) Attention-based graph neural networks: a survey. Artif Intell Rev 56(Suppl 2):2263–2310. https://doi.org/10.1007/s10462-023-10577-2

    Article  MATH  Google Scholar 

  30. Fan Y, Kukleva A, Dai D, Schiele B (2023) Revisiting consistency regularization for semi-supervised learning. Int J Comput Vision 131(3):626–643. https://doi.org/10.1007/s11263-022-01723-4

    Article  Google Scholar 

  31. Juan X, Zhou K, Liu N, Chen T, Wang X (2024) Molecular data programming: Towards molecule pseudo-labeling with systematic weak supervision. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp 308–318

  32. Liu Y, Xia L, Huang C (2024) Selfgnn: Self-supervised graph neural networks for sequential recommendation. In: Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, pp 1609–1618. https://doi.org/10.1145/3626772.3657716

  33. Hu Z, Zhou J, Wei W, Zhang C, Shi Y (2024) Predicting cross-domain collaboration using multi-task learning. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2024.124570

    Article  MATH  Google Scholar 

  34. Sun K, Lin Z, Zhu Z (2020) Multi-stage self-supervised learning for graph convolutional networks on graphs with few labeled nodes. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 34, pp 5892–5899. https://doi.org/10.1609/aaai.v34i04.6048

  35. Wang B, Li J, Liu Y, Cheng J, Rong Y, Wang W, Tsung F (2024) Deep insights into noisy pseudo labeling on graph data. Adv Neural Inf Process Syst 36:1–15. https://doi.org/10.5555/3666122.3669453

    Article  MATH  Google Scholar 

  36. Li Q, Chen L, Jing S, Wu D (2023) Pseudo-labeling with graph active learning for few-shot node classification. In: 2023 IEEE International Conference on Data Mining (ICDM). IEEE, pp 1115–1120. https://doi.org/10.1109/ICDM58522.2023.00133

  37. Xu J, Ren G, Tang J, Ding W, Wang G (2025) Selecting central and divergent samples via leading tree metric space for semi-supervised learning. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2025.3528400

    Article  MATH  Google Scholar 

  38. Liu C, Li X, Zhao D, Guo S, Kang X, Dong L, Yao H (2022) Graph neural networks with information anchors for node representation learning. Mob Netw Appl. https://doi.org/10.1007/s11036-020-01633-0

    Article  MATH  Google Scholar 

  39. Ju W, Fang Z, Gu Y, Liu Z, Long Q, Qiao Z, Qin Y, Shen J, Sun F, Xiao Z et al (2024) A comprehensive survey on deep graph representation learning. Neural Netw. https://doi.org/10.1016/j.neunet.2024.106207

    Article  MATH  Google Scholar 

  40. Li K, Feng Y, Gao Y, Qiu J (2020) Hierarchical graph attention networks for semi-supervised node classification. Appl Intell 50:3441–3451. https://doi.org/10.1007/s10489-020-01729-w

    Article  MATH  Google Scholar 

  41. He Z, Wan S, Zappatore M, Lu H (2024) A similarity matrix low-rank approximation and inconsistency separation fusion approach for multiview clustering. IEEE Trans Artif Intell 5(2):868–881. https://doi.org/10.1109/TAI.2023.3271964

    Article  MATH  Google Scholar 

  42. Li Y, Yin J, Chen L (2023) Informative pseudo-labeling for graph neural networks with few labels. Data Min Knowl Disc 37(1):228–254. https://doi.org/10.1007/s10618-022-00879-4

    Article  MATH  Google Scholar 

  43. Ma Z, Chen S (2022) A similarity-based framework for classification task. IEEE Trans Knowl Data Eng 35(5):5438–5443

    MATH  Google Scholar 

  44. Lu H, Jin T, Wei H, Nappi M, Li H, Wan S (2024) Soft-orthogonal constrained dual-stream encoder with self-supervised clustering network for brain functional connectivity data. Expert Syst Appl 244:122898–122908. https://doi.org/10.1109/TCE.2023.3279836

    Article  Google Scholar 

  45. Li Q, Han Z, Wu X-M (2018) Deeper insights into graph convolutional networks for semi-supervised learning. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol 32, pp 1–7. https://doi.org/10.1609/aaai.v32i1.11604

  46. Chen C, Lu H, Hong H, Wang H, Wan S (2023) Deep self-supervised graph attention convolution autoencoder for networks clustering. IEEE Trans Consum Electron 69(4):974–983. https://doi.org/10.1109/TCE.2023.3279836

    Article  MATH  Google Scholar 

  47. Xu J, Wang G, Deng W (2016) Denpehc: density peak based efficient hierarchical clustering. Inform Sci 373:200–218. https://doi.org/10.1016/j.ins.2016.08.086

    Article  MATH  Google Scholar 

  48. Xu J, Li T, Wu Y, Wang G (2021) Lapoleaf: label propagation in an optimal leading forest. Inf Sci 575:133–154. https://doi.org/10.1016/j.ins.2021.06.010

    Article  MathSciNet  MATH  Google Scholar 

  49. Xu J, Ren G, Xiao Y, Li S, Wang G (2022) Semi-supervised learning with deterministic labeling and large margin projection. arXiv preprint arXiv:2208.08058, 1–12 https://doi.org/10.48550/arXiv.2208.08058

  50. Chen J, Chen S, Bai M, Pu J, Zhang J, Gao J (2022) Graph decoupling attention markov networks for semisupervised graph node classification. IEEE Trans Neural Netw Learn Syst 34(12):9859–9873. https://doi.org/10.1109/TNNLS.2022.3161453

    Article  MATH  Google Scholar 

  51. Huang Z, Tang Y, Chen Y (2022) A graph neural network-based node classification model on class-imbalanced graph data. Knowl-Based Syst 244:108538–108549. https://doi.org/10.1016/j.knosys.2022.108538

    Article  MATH  Google Scholar 

  52. Ma G, Ahmed NK, Willke TL, Yu PS (2021) Deep graph similarity learning: a survey. Data Min Knowl Disc 35:688–725. https://doi.org/10.1007/s10618-020-00733-5

    Article  MathSciNet  MATH  Google Scholar 

  53. Xu G, Meng L (2023) A novel algorithm for identifying influential nodes in complex networks based on local propagation probability model. Chaos, Solitons & Fractals 168:113155–113168. https://doi.org/10.1016/j.chaos.2023.113155

    Article  MATH  Google Scholar 

  54. Feng J, Chen Y, Li F, Sarkar A, Zhang M (2022) How powerful are k-hop message passing graph neural networks. Adv Neural Inf Process Syst 35:4776–4790. https://doi.org/10.48550/arXiv.2205.13328

    Article  MATH  Google Scholar 

  55. Dou B, Zhu Z, Merkurjev E, Ke L, Chen L, Jiang J, Zhu Y, Liu J, Zhang B, Wei G-W (2023) Machine learning methods for small data challenges in molecular science. Chem Rev 123(13):8736–8780. https://doi.org/10.1021/acs.chemrev.3c00189

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grants No. 62366008, No. 61966005 and No. 62221005.

Author information

Authors and Affiliations

  1. State Key Laboratory of Public Big Data, Guizhou University, Guiyang, 550025, China

    Fuchuan Xiang, Yao Xiao, Fenglin Cen & Ji Xu

  2. College of Computer Science and Technology, Guizhou University, Guiyang, 550025, China

    Fuchuan Xiang & Ji Xu

Authors
  1. Fuchuan Xiang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yao Xiao
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Fenglin Cen
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Ji Xu
    View author publications

    You can also search for this author inPubMed Google Scholar

Contributions

Fuchuan Xiang contributed to methodology, investigation, software, writing-original draft, visualization. Yao Xiao and Fenglin Cen contributed to investigation, software, writing-original draft, visualization. Ji Xu contributed to conceptualization, supervision, investigation, review & editing, project administration, writing - review & editing.

Corresponding author

Correspondence to Ji Xu.

Ethics declarations

Conflict of interest

The authors declare that there does not exist any kind of Conflict of interest.

Ethical and informed consent for data used

This article does not contain studies with human participants or animals. Statement of informed consent is not applicable since the manuscript does not contain any patient data.

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 (e.g. a society or other partner) 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

Xiang, F., Xiao, Y., Cen, F. et al. SLRNode: node similarity-based leading relationship representation layer in graph neural networks for node classification. J Supercomput 81, 657 (2025). https://doi.org/10.1007/s11227-025-07094-0

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11227-025-07094-0

Keywords