Skip to main content
SpringerLink
Log in

Path-based estimation for link prediction

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

A Correction to this article was published on 20 July 2021

This article has been updated

Abstract

Link prediction has received a great deal of attention from researchers. Most of the existing researches are based on the network topology but ignore the importance of its preference; for aggregating multiple pieces of information, they normally sum up them directly. In this paper, a path-based probabilistic model is proposed to estimate the potential connectivity between any two nodes. It takes carefully the effective influence of nodes and the dependency among paths between two fixed nodes into account. Furthermore, we formulate the connectivity of two inner-community nodes and that of two inter-community nodes. The qualitative analysis shows that the links between inner-community nodes are more likely to be predicted by the proposed model. The performance is verified on both the multi-barbell network and Lesmis network. Considering the proposed model’s practicability, we develop an algorithm that iterates over the adjacent matrix to simulate paths of different lengths, with the parameters automatically grid-searched. The results of the experiments show that the proposed model outperforms competitive methods.

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
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Change history

Notes

  1. All pictures of networks in this paper are drawn by Gephi which is a software for the visualization of graphs and networks (http://networkrepository.com/index.php). Fruchterman Reingold [32] is used to generate the network layout, and the nodes in a network are colored by their modularities.

  2. These real networks can be downloaded at http://networkrepository.com/index.php.

References

  1. Adamic L, Adar E (2003) Friends and neighbors on the web. Soc Netw 25(3):211–230

    Article  Google Scholar 

  2. Aziz F, Gul H, Muhammad I, Uddin I (2020) Link prediction using node information on local paths. Phys Stat Mech Appl 557:124980

    Article  Google Scholar 

  3. Baird D, Ulanowicz R (1989) The seasonal dynamics of the Chesapeake bay ecosystem. Ecol Monogr 59(4):329–364

    Article  Google Scholar 

  4. Barabäsi A, Albert R (2009) Emergence and scaling in random networks. Science 106(52):22073–22078

    MathSciNet  Google Scholar 

  5. Batagelj V, Mrvar A (2000) Some analyses of Erdös collaboration graph. Soc Netw 22(2):173–186

    Article  Google Scholar 

  6. Brin S, Page L (1998) The anatomy of a large-scale hypertextual web search engine. Comput Netw ISDN Syst 30(1):107–117

    Article  Google Scholar 

  7. Cheng H, Ning Y, Yin Z, Yan C, Liu X, Zhang Z (2018) Community detection in complex networks using link prediction. Mod Phys Lett B 32(3):1850004

    Article  MathSciNet  Google Scholar 

  8. Curado M (2020) Return random walks for link prediction. Inf Sci 510:99–107

    Article  MathSciNet  Google Scholar 

  9. Fouss F, Pirotte A, Renders J, Saerens M (2007) Random-walk computation of similarities between nodes of a graph a graph with application to collaborative recommendation. IEEE Trans Knowl Data Eng 19(3):355–369

    Article  Google Scholar 

  10. Freeman L (1977) A set of measures of centrality based on betweenness. Sociometry 40(1):35–41

    Article  Google Scholar 

  11. Gao H, Ji S (2019) Graph u-nets. In: International conference on machine learning, pp 2083–2092

  12. Goyal P, Ferrara E (2017) Graph embedding techniques and applications and and performance: a survey. Knowl Based Syst 151:78

    Article  Google Scholar 

  13. Grover A, Leskovec J (2016) node2vec: Scalable feature learning for networks. In: Proceedings of the 22nd ACM International conference on knowledge discovery and data mining

  14. Guo J, Shi L, Liu L (2019) Node degree and neighbourhood tightness based link prediction in social networks. In: 2019 9th International conference on information science and technology (ICIST), IEEE, pp 135–140

  15. Hanely J, McNeil B (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29–36

    Article  Google Scholar 

  16. Hasan MA, Zaki M (2011) A survey of link prediction in social networks. In Social network data analytics. Springer, New York, pp 243–275

    Google Scholar 

  17. Jalili M, Orouskhani Y, Asgari M, Alipourfard N, Perc M (2017) Link prediction in multiplex online social networks. R Soc Open Sci 4(2):160863

    Article  MathSciNet  Google Scholar 

  18. Jeh G, Widom J (2002) Simrank: a measure of structural-context similarity. In: Eighth ACM SIGKDD International conference on knowledge discovery and data mining, pp 538–543

  19. Klein D, Randic M (1993) Resistance distance. J Math Chem 12(1):81–95

    Article  MathSciNet  Google Scholar 

  20. Lebedev A, Lee J, Rivera V, Mazzara M (2017) Link prediction using top-k shortest distances. In: British International conference on databases, Springer, pp 101–105

  21. Li Y, Luo P, Fan Z, Chen K, Liu J (2017) A utility-based link prediction method in social networks. Eur J Oper Res 260(2):693–705

    Article  MathSciNet  MATH  Google Scholar 

  22. Lichtenwalter R, Lussier J, Chawla N (2010) New perspectives and methods in link prediction. In: Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 243–252

  23. Liu W, Lü L (2010) Link prediction based on local random walk. Europhys Lett 89(5):58007

    Article  Google Scholar 

  24. Liu W, Gong M, Wang S, Ma L (2018) A two-level learning strategy based memetic algorithm for enhancing community robustness of networks. Inf Sci 422:290–304

    Article  Google Scholar 

  25. Lorrain F, White H (1977) Structural equivalence of individuals in social networks. Soc Netw 1(1):67–98

    Article  Google Scholar 

  26. Lü L, Zhou T (2011) Link prediction in complex networks: a survey. Phys A Stat Mech Appl 390(6):1150–1170

    Article  Google Scholar 

  27. Lü L, Jin C, Zhou T (2009) Similarity index based on local path for link prediction of complex networks. Phys Rev E 80(4):046122

    Article  Google Scholar 

  28. Ma C, Zhou T, Zhang H (2016) Playing the role of weak clique property in link prediction: a friend recommendation model. Sci Rep 6:1

    Google Scholar 

  29. Mallek S, Boukhris I, Elouedi Z, Lefevre E (2017) Evidential k-nn for link prediction. In: European conference on symbolic and quantitative approaches to reasoning and uncertainty, Springer, pp 201–211

  30. Manshad M, Meybodi M, Salajegheh A (2020) A new irregular cellular learning automata-based evolutionary computation for time series link prediction in social networks. Appl Intell 51:1–14

    Google Scholar 

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

    Article  Google Scholar 

  32. Mennens R, Scheepens R, Westenberg MA (2019) A stable graph layout algorithm for processes. Comput Graphics Forum 38(3):725–737

    Article  Google Scholar 

  33. Mering CV, Krause R, Snel B, Cornell M, Stephen GO, Fields S, Bork P (2002) Comparative assessment of large-scale data sets of protein–protein interactions. Nature 417:399–403

    Article  Google Scholar 

  34. Ou M, Peng C, Jian P, Zhang Z, Zhu W (2016) Asymmetric transitivity preserving graph embedding. In: The 22nd ACM SIGKDD International conference

  35. Qian Y, Jiye L, Witold P, Dang C (2010) Positive approximation: an accelerator for attribute reduction in rough set theory. Artif Intell 174(9–10):597–618

    Article  MathSciNet  MATH  Google Scholar 

  36. Rossi R, Ahmed N (2015) The network data repository with interactive graph analytics and visualization. In: Proceedings of the twenty-ninth AAAI conference on artificial intelligence. http://networkrepository.com

  37. Sarukkai R (2000) Link prediction and path analysis using Markov chains. Comput Netw 33(1–6):377–386

    Article  Google Scholar 

  38. Soffer S, Vazquez A (2005) Network clustering coefficient without degree-correlation biases. Phys Rev E 71(5):057101

    Article  Google Scholar 

  39. Sun B, Shen H, Gao J, Ouyang W, Cheng X (2017) A non-negative symmetric encoder–decoder approach for community detection. In: Proceedings of the 2017 ACM on conference on information and knowledge management. https://doi.org/10.1145/3132847.3132902

  40. Tian Y, Li H, Zhu X, Tian H (2019) Link prediction based on combined influence and effective path. Int J Mod Phys B 33(22):1950249

    Article  Google Scholar 

  41. Tong H, Faloutsos C, Pan J (2006) Fast random walk with restart and its applications. In: Sixth international conference on data mining (ICDM’06), IEEE, pp 613–622

  42. Šubelj L, Bajec M (2011) Robust network community detection using balanced propagation. Eur Phys J B 81(3):353–362

    Article  Google Scholar 

  43. Wang D, Peng C, Zhu W (2016a) Structural deep network embedding. In: the 22nd ACM SIGKDD International conference

  44. Wang L, Ren J, Xu B, Li J, Luo W, Xia F (2020) Model: Motif-based deep feature learning for link prediction. IEEE Trans Comput Soc Syst 7(2):503–516

    Article  Google Scholar 

  45. Wang P, Xu B, Wu Y, Zhou X (2015) Link prediction in social networks: the state-of-the-art. Sci China Inf Sci 58(1):1–38

    Article  Google Scholar 

  46. Wang X, Cui P, Wang J, Pei J, Zhu W, Yang S (2017) Community preserving network embedding. In: Thirty-first AAAI conference on artificial intelligence

  47. Wang Z, Liang J, Li R, Qian Y (2016b) An approach to cold-start link prediction: establishing connections between non-topological and topological information. IEEE Trans Knowl Data Eng 28(11):2857–2870

    Article  Google Scholar 

  48. Watts D, Steven H (1998) Collective dynamics of small world networks. Nature 393:440–442

    Article  MATH  Google Scholar 

  49. White J, Southgate E, Thomson J et al (1976) The structure of the ventral nerve cord of Caenorhabditis elegans. Philos Trans R Soc Lond 275(938):327

    Google Scholar 

  50. Xie F, Chen Z, Shang J, Feng X, Li J (2015) A link prediction approach for item recommendation with complex number. Knowl Based Syst 81(C):148–158

    Article  Google Scholar 

  51. Xie Y, Zhou T, Wang B (2008) Scale-free networks without growth. Phys A Stat Mech Appl 387(7):1683

    Article  Google Scholar 

  52. Xie Y, Gong M, Wang S, Yu B (2018) Community discovery in networks with deep sparse filtering. Pattern Recognit 81:50–59

    Article  Google Scholar 

  53. Yao Y, Zhang R, Yang F, Tang J, Yuan Y, Hu R (2018) Link prediction in complex networks based on the interactions among paths. Phys A Stat Mech Appl 510:52–67

    Article  Google Scholar 

  54. Zhang M, Chen Y (2018) Link prediction based on graph neural networks. In: Advances in Neural information processing systems, pp 5165–5175

  55. Zhao Z, Zheng S, Li C, Sun J, Chang L, Francisco C (2018) A comparative study on community detection methods in complex networks. J Intell Fuzzy Syst 35(1):1077–1086

    Article  Google Scholar 

  56. Zhao Z, Li C, Zhang X, Chiclana F, Enrique HV (2019) An incremental method to detect communities in dynamic evolving social networks. Knowl Based Syst 163:404–415

    Article  Google Scholar 

  57. Zhong Z, Zhang Y, Pang J (2020) Neulp: An end-to-end deep-learning model for link prediction. In: International conference on web information systems engineering, Springer, pp 96–108

  58. Zhu X, Tian H, Cai S (2014) Predicting missing links via effective paths. Phys A Stat Mech Appl 413(11):515–522

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Yayu Zhang, Furong Lu, Honghong Cheng, Jieting Wang and Junjie Ma for their insightful discussions. This work was supported by National Natural Science Foundation of China (nos. 61672332, 61322211, 61432011, 61872226 and U1435212), the Young Scientists Fund of the National Natural Science Foundation of China (Grant no. 61802238). Program for New Century Excellent Talents in University (no. NCET-12-1031), Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, and Program for the Young San Jin Scholars of Shanxi, the Natural Science Foundation of Shanxi Province (no. 201701D121052), the Research Project Supported by Shanxi Scholarship Council of China (no. 2017023).

Author information

Author notes

  1. Guoshuai Ma and Hongren Yan contributed equally to this work.

Authors and Affiliations

  1. Institute of Big Data Science and Industry, Shanxi University, Taiyuan, 030006, Shanxi, China

    Guoshuai Ma, Hongren Yan & Yuhua Qian

  2. School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, China

    Guoshuai Ma, Hongren Yan & Yuhua Qian

  3. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006, Shanxi, China

    Yuhua Qian

  4. Department of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA

    Lingfeng Wang

  5. Department of Manufacture Engineering and Engineering Management, City University of Hong Kong, Kowloon Tong, Hong Kong

    Chuangyin Dang

  6. The School of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Zhongying Zhao

Authors
  1. Guoshuai Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongren Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuhua Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lingfeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chuangyin Dang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Zhongying Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuhua Qian.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, G., Yan, H., Qian, Y. et al. Path-based estimation for link prediction. Int. J. Mach. Learn. & Cyber. 12, 2443–2458 (2021). https://doi.org/10.1007/s13042-021-01312-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-021-01312-w

Keywords

Search

Navigation