Skip to main content
Log in

An attentional-walk-based autoencoder for community detection

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

The purpose of community detection is to discover closely connected groups of entities in complex networks such as interest groups, proteins and vehicles in social, biological and transportation networks. Recently, autoencoders have become a popular technique to extract nonlinear relationships between nodes by learning their representation vectors through an encoder-decoder neural structure, which is beneficial to discovering communities with vague boundaries. However, most of the existing autoencoders take restoring a network’s adjacency matrix as their objective, which puts emphasis on the first-order relationships between the nodes and neglects their higher-order relationships that may be more useful for community detection. In this paper, we propose a novel attentional-walk-based autoencoder (AWBA) which integrates random walk considering attentional coefficients between each pair of nodes into the encoder to mine their high-order relationships. First, the attention layers are added to the encoder to learn the influence of a node’s different neighbors on it in encoding. Second, we develop a new random walk strategy that embeds the attention coefficients and the community membership of the nodes obtained by a seed-expansion-based clustering algorithm into the computation of the transition probability matrix to instill both low and high order relationships between the nodes into the representation vectors. The experimental results on synthetic and real-world networks verify the superiority of our algorithm over the baseline algorithms.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

Notes

  1. The source code of AWBA, the competitor algorithms, the LFR tool and the evaluation metrics are available at https://anonymous.4open.science/r/awba-0C48.

  2. The networks were put at https://anonymous.4open.science/r/community-detection-datasets-5D1F.

  3. The source code of AWBA, the competitor algorithms, the LFR tool and the evaluation metrics are available at https://anonymous.4open.science/r/awba-0C48.

References

  1. Fortunato S. (2010) Community detection in graphs[J]. Phys Rep 486(3-5):75–174

    Article  MathSciNet  Google Scholar 

  2. Newman M E J (2004) Fast algorithm for detecting community structure in networks[J]. Phys Rev E, 69(6):066133

  3. Barber M J, Clark J W (2009) Detecting network communities by propagating labels under constraints[J]. Phys Rev E, 80(2):026129

  4. Khan B S, Niazi M A (2017) Network community detection: A review and visual survey[J]. arXiv:1708.00977

  5. Palla G, Derényi I, Farkas I, et al. (2005) Uncovering the overlapping community structure of complex networks in nature and society[J]. Nature 435(7043):814–818

    Article  Google Scholar 

  6. Lancichinetti A, Fortunato S, Kertész J (2009) Detecting the overlapping and hierarchical community structure in complex networks[J]. J Phys 11(3):033015

  7. Evans T S, Lambiotte R (2009) Line graphs, link partitions, and overlapping communities[J]. Phys Rev E, 80(1):016105

  8. Lloyd S. (1982) Least squares quantization in PCM [J]. IEEE Trans Inf Theory 28(2):129–137

    Article  MathSciNet  MATH  Google Scholar 

  9. Yang Z, Ding M, Zhou C, et al. (2020) Understanding negative sampling in graph representation learning[C]//Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp 1666–1676

  10. Perozzi B, Al-Rfou R, Skiena S (2014) Deepwalk: Online learning of social representations[C]//Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 701–710

  11. Mikolov T, Sutskever I, Chen K, et al. (2013) Distributed representations of words and phrases and their compositionality[C]//Advances in neural information processing systems, pp 3111–3119

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

  13. Tu C, Zeng X, Wang H, et al. (2018) A unified framework for community detection and network representation learning [J]. IEEE Trans Knowl Data Eng 31(6):1051–1065

    Article  Google Scholar 

  14. Huang X, Song Q, Yang F, et al. (2019) Large-scale heterogeneous feature embedding[C]. Proc AAAI Conf Artif Intell 33(01):3878–3885

    Google Scholar 

  15. Li G, Muller M, Thabet A, et al. (2019) Deepgcns: Can gcns go as deep as cnns. [C]//Proceedings of the IEEE/CVF International Conference on Computer Vision, pp 9267–9276

  16. Li G, Xiong C, Thabet A, et al. (2020) Deepergcn: All you need to train deeper gcns[J]. arXiv:2006.07739

  17. Cai C, Wang Y. (2020) A note on over-smoothing for graph neural networks[J]. arXiv:2006.13318

  18. Veličković P, Cucurull G, Casanova A, et al. (2017) Graph attention networks[J]. arXiv:1710.10903

  19. Abu-El-Haija S, Perozzi B, Al-Rfou R, et al. (2017) Watch your step: Learning node embeddings via graph attention[J]. arXiv:1710.09599

  20. Grover A, Leskovec J (2016) node2vec: Scalable feature learning for networks[C]//Proceedings of the 22nd ACM SIGKDD international conference on Knowledge discovery and data mining, pp 855–864

  21. Tang J, Qu M, Wang M, et al. (2015) Line: Large-scale information network embedding[C]//Proceedings of the 24th international conference on world wide web. 1067–1077

  22. Zhang D, Yin J, Zhu X, et al. (2019) Attributed network embedding via subspace discovery[J]. Data Min Knowl Disc 33(6):1953–1980

    Article  MATH  Google Scholar 

  23. Bandyopadhyay S, Biswas A, Kara H, et al. (2020) A multilayered informative random walk for attributed social network embedding[M]//ECAI 2020. IOS Press:1738–1745

  24. Hamilton W L, Ying R, Leskovec J (2017) Inductive representation learning on large graphs[C]//Proceedings of the 31st International Conference on Neural Information Processing Systems, pp 1025–1035

  25. Xu K, Hu W, Leskovec J, et al. (2018) How powerful are graph neural networks?[J]. arXiv:1810.00826

  26. You J, Ying R, Leskovec J. (2019) Position-aware graph neural networks [C]//International Conference on Machine Learning. PMLR, pp 7134–7143

  27. Kingma D P, Welling M. (2013) Auto-encoding variational bayes[J]. arXiv:1312.6114

  28. Kipf T N, Welling M. (2016) Variational graph auto-encoders[J]. arXiv:1611.07308

  29. Pan S, Hu R, Long G, et al. (2018) Adversarially regularized graph autoencoder for graph embedding[J]. arXiv:1802.04407

  30. Wang C, Pan S, Long G, et al. (2017) Mgae: Marginalized graph autoencoder for graph clustering[C]//Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, pp 889–898

  31. Park J, Lee M, Chang HJ, et al. (2019) Symmetric graph convolutional autoencoder for unsupervised graph representation learning[C]//Proceedings of the IEEE/CVF International Conference on Computer Vision, pp 6519–6528

  32. Cui G, Zhou J, Yang C (2020) Adaptive graph encoder for attributed graph embedding[C]//Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp 976–985

  33. Cavallari S, Zheng V W, Cai H, et al. (2017) Learning community embedding with community detection and node embedding on graphs[C]//Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, pp 377–386

  34. Rozemberczki B, Davies R, Sarkar R, et al. (2019) Gemsec: Graph embedding with self clustering[C]//Proceedings of the 2019 IEEE/ACM international conference on advances in social networks analysis and mining, pp 65–72

  35. Sun F Y, Qu M, Hoffmann J, et al. (2019) vgraph: A generative model for joint community detection and node representation learning[J]. arXiv:1906.07159

  36. Jia Y, Zhang Q, Zhang W, et al. (2019) Communitygan: Community detection with generative adversarial nets[C]//The World Wide Web Conference, pp 784–794

  37. Sun H, He F, Huang J, et al. (2020) Network embedding for community detection in attributed networks [J]. ACM Trans Knowl Discov Data (TKDD) 14(3):1–25

    Article  Google Scholar 

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

  39. Zachary W. W. (1977) An information flow model for conflict and fission in small groups [J]. J Anthropol Res 33(4):452–473

    Article  Google Scholar 

  40. Lusseau D, Schneider K, Boisseau O J, et al. (2003) The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations [J]. Behav Ecol Sociobiol 54(4):396–405

    Article  Google Scholar 

  41. Girvan M, Newman M. E. J. (2002) Community structure in social and biological networks [J]. Proc Ntl Acad Sci 99(12):7821–7826

    Article  MathSciNet  MATH  Google Scholar 

  42. Newman M E J, Girvan M (2004) Finding and evaluating community structure in networks[J]. Phys Rev E 69(2):026113

  43. Adamic L A, Glance N (2005) The political blogosphere and the 2004 US election: divided they blog[C]//Proceedings of the 3rd international workshop on Link discovery, pp 36–43

  44. McCallum A K, Nigam K, Rennie J, et al. (2000) Automating the construction of internet portals with machine learning [J]. Inf Retr 3(2):127–163

    Article  Google Scholar 

  45. Yang C, Liu Z, Zhao D, et al. (2015) Network representation learning with rich text information [C]//Twenty-fourth international joint conference on artificial intelligence

  46. Tang L, Liu H (2009) Relational learning via latent social dimensions[C]//Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 817–826

  47. Danon L, Diaz-Guilera A, Duch J, et al. (2005) Comparing community structure identification [J]. J Stat Mech Theory Exper 2005(09):P09008

    Article  Google Scholar 

  48. Tian F, Gao B, Cui Q et al (2014) Learning deep representations for graph clustering[C]//Proceedings of the AAAI Conf Artif Intell 28(1)

  49. Van der Maaten L, Hinton G (2008) Visualizing data using t-SNE[J]. J Mach Learn Res 9(11)

  50. Yang L, Cao X, He D, et al. (2016) Modularity Based Community Detection with Deep Learning[C]. IJCAI 16:2252–2258

    Google Scholar 

  51. He D, Feng Z, Jin D, et al. (2017) Joint identification of network communities and semantics via integrative modeling of network topologies and node contents [C]//Thirty-First AAAI Conference on Artificial Intelligence

  52. Jin D, Wang X, He R et al (2018) Robust detection of link communities in large social networks by exploiting link semantics[C]//Proc AAAI Conf Artif Intell 32(1)

  53. Qin M, Jin D, Lei K, et al. (2018) Adaptive community detection incorporating topology and content in social networks [J]. Knowl-based Syst 161:342–356

    Article  Google Scholar 

  54. Li Y, Sha C, Huang X et al (2018) Community detection in attributed graphs: An embedding approach[C]//Thirty-second AAAI conference on artificial intelligence

  55. Qin M, Lei K. (2021) Dual-channel hybrid community detection in attributed networks[J]. Inf Sci 551:146–167

    Article  MathSciNet  MATH  Google Scholar 

  56. Li W, Qin M, Lei K (2019) Identifying Interpretable Link Communities with User Interactions and Messages in Social Networks[C]//2019 IEEE Intl Conf on Parallel & Distributed Processing with Applications, Big Data & Cloud Computing, Sustainable Computing & Communications, Social Computing & Networking (ISPA/BDCloud/SocialCom/SustainCom). IEEE, pp 271–278

  57. Ye F, Chen C, Zheng Z (2018) Deep autoencoder-like nonnegative matrix factorization for community detection[C]//Proceedings of the 27th ACM international conference on information and knowledge management, pp 1393–1402

  58. Mehta N, Duke L C, Rai P. (2019) Stochastic blockmodels meet graph neural networks[C]//International Conference on Machine Learning. PMLR, pp 4466–4474

  59. Blondel V D, Guillaume J L, Lambiotte R, et al. (2008) Fast unfolding of communities in large networks[J]. J Stat Mech Theory Exper 2008(10):P10008

    Article  MATH  Google Scholar 

  60. Xie J, Szymanski B K, Liu X. (2011) Slpa: Uncovering overlapping communities in social networks via a speaker-listener interaction dynamic process[C]//2011 ieee 11th international conference on data mining workshops. IEEE, pp 344–349

  61. Qian F, et al., Huang X, Zhao S (2019) Path-based mutual attention algorithm for network embedding[J] Journal of Nanjing University(Natural Science)

  62. GUO J, DONG H, ZHANG T, et al. (2020) Representation learning for topic-attention network[J]. J Comput Appl 40(2):441–447

    Google Scholar 

  63. Moscato V, Picariello A, Sperlí G (2019) Community detection based on game theory[J]. Eng Appl Artif Intell 85:773–782

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuzhong Chen.

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

Guo, K., Zhang, P., Guo, W. et al. An attentional-walk-based autoencoder for community detection. Appl Intell 53, 11505–11523 (2023). https://doi.org/10.1007/s10489-021-02957-4

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-021-02957-4

Keywords

Navigation