Skip to main content
SpringerLink
Log in

Graph attention network via node similarity for link prediction

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Link prediction is a classic complex network analytical problem to predict the possible links according to the known network structure information. Considering similar nodes should present closer embedding vectors with network representation learning, in this paper, we propose a Graph ATtention network method based on node Similarity (SiGAT) for link prediction. Specifically, we calculate similar node set for each node in the network by traditional method. The similar nodes and first-order neighbors are assigned an optimal weight through the graph attention network mechanism. Then, we obtain the embedding vectors of nodes with aggregating the information of the similar nodes and first-order neighbor nodes. By incorporating similar nodes, the node embeddings preserve more structure information of the network in low-dimensional embedding space. Finally, the SiGAT represents the links between pairs of nodes with concatenating the node embedding vectors and then trains a classifier to predict novel potential network links. The results of experiments on five real datasets and large-scale artificial datasets, which are the Yeast dataset, Cora dataset, BIO-CE-HT dataset, Human proteins (Vidal) dataset, Human proteins (Stelzl) dataset, and LFR benchmark datasets, show that the SiGAT outperforms the existing popular approaches.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data availability statement

This manuscript has associated data in a data repository. Readers can find the main code and datasets for this paper at the following websites. https://github.com/wefwfrfg/SiGAThttp://konect.cc/networks/https://networkrepository.com/bio.phphttps://linqs-data.soe.ucsc.edu/public/lbc/cora.tgz.

References

  1. L. Lü, T. Zhou, Link prediction in complex networks: a survey. Physica A 390(6), 1150–1170 (2011)

    Article  ADS  Google Scholar 

  2. K. Berahmand, E. Nasiri, S. Forouzandeh, Y. Li, A preference random walk algorithm for link prediction through mutual influence nodes in complex networks. Eur. J. Inform. Syst. 34(8), 5375–5387 (2022)

    Google Scholar 

  3. E. Nasiri, K. Berahmand, Y. Li, Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks. Multim. Tools. Appl. 82(3), 3745–3768 (2023)

    Article  Google Scholar 

  4. J. Vamathevan, D. Clark, P. Czodrowski, I. Dunham, E. Ferran, G. Lee, B. Li, A. Madabhushi, P. Shah, M. Spitzer et al., Applications of machine learning in drug discovery and development. Nat. Rev. Drug Discov. 18(6), 463–477 (2019)

    Article  Google Scholar 

  5. V. Agarwal, K.K. Bharadwaj, A collaborative filtering framework for friends recommendation in social networks based on interaction intensity and adaptive user similarity. Soc. Netw. Anal. Min. 3(3), 359–379 (2013)

    Article  Google Scholar 

  6. T. Zhou, L. Lü, Y.-C. Zhang, Predicting missing links via local information. Eur. Phys. J. B 71(4), 623–630 (2009)

    Article  ADS  MATH  Google Scholar 

  7. L. Yao, L. Wang, L. Pan, K. Yao, Link prediction based on common-neighbors for dynamic social network. Procedia Comput. Sci. 83, 82–89 (2016)

    Article  Google Scholar 

  8. E. Nasiri, K. Berahmand, Z. Samei, Y. Li, Impact of centrality measures on the common neighbors in link prediction for multiplex networks. Big Data 10(2), 138–150 (2022)

    Article  Google Scholar 

  9. W. Zhou, J. Gu, Y. Jia, h-index-based link prediction methods in citation network. Scientometrics 117(1), 381–390 (2018)

    Article  Google Scholar 

  10. V. Martínez, F. Berzal, J.-C. Cubero, A survey of link prediction in complex networks. ACM Comput. Surv. 49(4), 1–33 (2016)

    Article  Google Scholar 

  11. L. Katz, A new status index derived from sociometric analysis. Psychometrika 18(1), 39–43 (1953)

    Article  MATH  Google Scholar 

  12. G. Nikolentzos, M. Vazirgiannis, Random walk graph neural networks. Adv. Neural Inf. Process. Syst. 33, 16211–16222 (2020)

    Google Scholar 

  13. L. Page, S. Brin, R. Motwani, T. Winograd, The pagerank citation ranking: Bringing order to the web (Tech. rep, Stanford InfoLab, 1999)

  14. H. Tong, C. Faloutsos, J.-Y. Pan, Fast random walk with restart and its applications. In Proceedings of the Sixth International Conference on Data Mining, pp. 613–622 (2006)

  15. S. Pal, Y. Dong, B. Thapa, N.V. Chawla, A. Swami, R. Ramanathan, Deep learning for network analysis: problems, approaches and challenges. In: Proceedings of the IEEE Military Communications Conference, pp. 588–593 (2016)

  16. B. Perozzi, R. Al-Rfou, S. Skiena, Deepwalk: online learning of social representations. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 701–710 (2014)

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

    Article  Google Scholar 

  18. M. Coşkun, M. Koyutürk, Node similarity-based graph convolution for link prediction in biological networks. Bioinformatics 37(23), 4501–4508 (2021)

    Article  Google Scholar 

  19. T.N. Kipf, M. Welling, Semi-supervised classification with graph convolutional networks. arXiv:1609.02907 (2016)

  20. J. Zhou, G. Cui, S. Hu, Z. Zhang, C. Yang, Z. Liu, L. Wang, C. Li, M. Sun, Graph neural networks: a review of methods and applications. AI Open 1, 57–81 (2020)

    Article  Google Scholar 

  21. X. Xian, L. Fang, S. Sun, Regnn: a repeat aware graph neural network for session-based recommendations. IEEE Access 8, 98518–98525 (2020)

    Article  Google Scholar 

  22. D. Liben-Nowell, J. Kleinberg, The link-prediction problem for social networks. J. Assoc. Inf. Sci. Technol. 58(7), 1019–1031 (2007)

    Article  Google Scholar 

  23. S. Bhagat, G. Cormode, S. Muthukrishnan, Node classification in social networks. Soc. Netw. Anal. Min. 115–148 (2011)

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

  25. R. Real, J.M. Vargas, The probabilistic basis of Jaccard’s index of similarity. Syst. Biol. 45(3), 380–385 (1996)

    Article  Google Scholar 

  26. M. Pal, Random forest classifier for remote sensing classification. Int. J. Remote Sens. 26(1), 217–222 (2005)

    Article  Google Scholar 

  27. M. Zhang, Y. Chen, Link prediction based on graph neural networks. Adv. Neural Inf. Process. Syst. 31 (2018)

  28. W. Shen, Y. Chen, Y. Cheng, K. Yang, X. Guo, Y. Sun, Y. Chen, An improved deep-learning model for road extraction from very-high-resolution remote sensing images. In: Proceedings of the IEEE International Symposium on Geoscience and Remote Sensing, pp. 4660–4663 (2021)

  29. Z. Yang, M. Ding, C. Zhou, H. Yang, J. Zhou, J. Tang, Understanding negative sampling in graph representation learning. arXiv:2005.09863 (2020)

  30. X. Xu, B. Liu, J. Wu, L. Jiao, Link prediction in complex networks via matrix perturbation and decomposition. Sci. Rep. 7(1), 1–9 (2017)

    Google Scholar 

  31. X. Huang, J. Li, X. Hu, Accelerated attributed network embedding, in: Proc. SIAM Int. Conf. Data Mining., pp. 633–641 (2017)

  32. J. Tang, M. Qu, M. Wang, M. Zhang, J. Yan, Q. Mei, Line: Large-scale information network embedding, in: Proceedings of the 24th International Conference on World Wide Web, pp. 1067–1077 (2015)

  33. A.P. Bradley, The use of the area under the roc curve in the evaluation of machine learning algorithms. Pattern Recognit. 30(7), 1145–1159 (1997)

  34. I. Yaniv, D.P. Foster, Precision and accuracy of judgmental estimation. J. Behav. Decis. Mak. 10(1), 21–32 (1997)

    Article  Google Scholar 

  35. J. Davis, M. Goadrich, The relationship between precision-recall and roc curves, in: Proc. 23rd Int. Conf. Machine Learning, pp. 233–240 (2006)

  36. Z. C. Lipton, C. Elkan, B. Narayanaswamy, Thresholding classifiers to maximize f1 score, arXiv:1402.1892 (2014)

  37. J. Kunegis, KONECT – The Koblenz Network Collection, in: Proceedings of the 22nd International Conference on World Wide Web, pp. 1343–1350 (2013)

  38. R. A. Rossi, N. K. Ahmed, The network data repository with interactive graph analytics and visualization, in: Proceedings of the 29th AAAI Conference on Artificial Intelligence, (2015)

  39. A.K. McCallum, K. Nigam, J. Rennie, K. Seymore, Automating the construction of internet portals with machine learning. J. Inf. Sci. 3(2), 127–163 (2000)

    Google Scholar 

  40. K. Diederik, B. Jimmy, et al., Adam: a method for stochastic optimization. arXiv:1412.6980 (2014)

  41. A. Mayr, B. Hofner, M. Schmid, The importance of knowing when to stop. Methods Inf. Med. 51(02), 178–186 (2012)

    Article  Google Scholar 

  42. A. Lancichinetti, S. Fortunato, F. Radicchi, Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)

  43. A.J. Scott, M. Knott, A cluster analysis method for grouping means in the analysis of variance. Biometrics 507–512 (1974)

  44. F.O. Isinkaye, Y.O. Folajimi, B.A. Ojokoh, Recommendation systems: principles, methods and evaluation. Egypt. Inform. J. 16(3), 261–273 (2015)

    Article  Google Scholar 

  45. C. Shi, Y. Li, J. Zhang, Y. Sun, S.Y. Philip, A survey of heterogeneous information network analysis. IEEE Trans. Knowl. Data. Eng. 29(1), 17–37 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge anonymous reviewers for their time and effort in reviewing this paper. This work is supported in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 22KJD120002).

Author information

Authors and Affiliations

  1. College of Information Engineering, Yangzhou University, Yangzhou, 225127, China

    Kai Yang, Yuan Liu, Xingxing Zhou & Peijin Ding

  2. Business School, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Zijuan Zhao

Authors
  1. Kai Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zijuan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xingxing Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Peijin Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

KY and YL: conceptualization, methodology, data curation, writing, visualization, and investigation. ZZ, XZ and PD: supervision, reviewing, and editing.

Corresponding author

Correspondence to Kai Yang.

Additional information

This work was partially supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 22KJD120002.

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

Yang, K., Liu, Y., Zhao, Z. et al. Graph attention network via node similarity for link prediction. Eur. Phys. J. B 96, 27 (2023). https://doi.org/10.1140/epjb/s10051-023-00495-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-023-00495-1

Search

Navigation