Abstract
The idea of predicting links in multiplex networks has gained increasing interest in recent years. In this paper, we propose a comprehensive framework which benefits from the structural information of auxiliary layers to predict links on a target layer of multiplex networks. Specifically, we assume that the likelihood of the existence of a link between two nodes is determined by the contributions from both the nodes’ neighbors on the target layer and their counterparts’ neighbors on a manually network generated by auxiliary layers. The final likelihood matrix is acquired by an iterative algorithm. In addition, we show advantages of our methods for predicting links on sparse and dense networks as well as on networks with assortative and disassortative structural layers. The effectiveness of the proposed methods are evaluated through extensive experiments on real-world multiplex networks.
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References
Abdolhosseini Q, Amir M, Naser Y, Masoud A (2020) Overlapping communities and the prediction of missing links in multiplex networks. Phys A: Stat Mech Appl 554:124650
Adamic LA, Adar E (2003) Friends and neighbors on the web. Soc Netw 25(3):211–230
Aiello LM et al (2012) Friendship prediction and homophily in social media. ACM Transact Web (TWEB) 6(2):1–33
Al Hasan M, et al (2006) Link prediction using supervised learning. In: SDM06: workshop on link analysis, counter-terrorism and security 30: 798-805
Bargigli L et al (2015) The multiplex structure of interbank networks. Quant Financ 15:673–691
Bassett DS, Sporns O (2017) Network neuroscience. Nat Neurosci 20(3):353–364
Chen J et al (2019) E-lstm-d: A deep learning framework for dynamic network link prediction. IEEE Transact Syst, Man, and Cybernet: Syst 51(6):3699–3712
Chuan PM et al (2018) Link prediction in co-authorship networks based on hybrid content similarity metric. Appl Intell 48(8):2470–2486
Coleman J, Katz E, Menzel H (1957) The Diffusion of an Innovation Among Physicians. Sociometry 20:253–270
Cui P, Wang X, Pei J, Zhu W (2019) A survey on network embedding. IEEE Transact Knowl Data Eng 31(5):833–852
Davis D, Lichtenwalter R, Chawla N V (2011) Multi-relational link prediction in heterogeneous information networks. In: 2011 International conference on advances in social networks analysis and mining. IEEE, 281-288
De Bacco C, Power EA, Larremore DB, Moore C (2017) Community detection, link prediction, and layer interdependence in multilayer networks. Phys Rev E 95(4):042317
De Domenico M, Nicosia V, Arenas A, Latora V (2015) Structural reducibility of multilayer networks. Nat Communicat 6:6864
De Domenico M, Solé-Ribalta A, Gómez S, Arenas A (2014) Navigability of interconnected networks under random failures. PNAS 111:8351–8356
Goyal P, Ferrara E (2018) Graph embedding techniques, applications, and performance: A survey. Knowl-Based Syst 151:78–94
Hanley JA, Mcneil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143(1):29–36
Hristova D et al (2016) A multilayer approach to multiplexity and link prediction in online geo-social networks. EPJ Data Sci 5(1):24
Jalili M, Orouskhani Y, Asgari M et al (2017) Link prediction in multiplex online social networks. Royal Soc Open Sci 4(2):160863
Jones S (2006) Terrorism in Indonesia: Noordin’s Networks. Asia Report 114
Kao TC, Porter MA (2018) Layer communities in multiplex networks. J Stat Phys 173(3–4):1286–1302
Kapferer B (1972) Strategy and transaction in an African factory: African workers and Indian management in a Zambian town. Manchester University Press, Manchester
Katz L (1953) A new status index derived from sociometric analysis. Psychometrika 18(1):39–43
Kivelä M et al (2014) Multilayer networks. Journal of Complex. Networks 2(3):203–271
Kleineberg KK, Boguã M, Ángeles Serrano M, Papadopoulos F (2016) Hidden geometric correlations in real multiplex networks. Nat Phys 12:1076–1081
Kovács IA et al (2019) Network-based prediction of protein interactions. Nat Commun 10:1240
Lazega E (2001) The collegial phenomenon: The social mechanisms of cooperation among peers in a corporate law partnership. Oxford University Press on Demand, Oxford
Leicht EA, Holme P, Newman MEJ (2006) Vertex similarity in networks. Phys Rev E 73(2):026120
Lü L et al (2012) Recommender systems. Phys Rep 519(1):1–49
Lü L, Zhou T (2011) Link prediction in complex networks: A survey. Phys A: stat Mech Appl 390(6):1150–1170
Magnani M, Micenkova B, Rossi L. (2013) Combinatorial analysis of multiple networks. arXiv preprint arXiv:1303.4986
Najari S, Salehi M, Ranjbar V et al (2019) Link prediction in multiplex networks based on interlayer similarity. Phys A: Stat Mech Appl 536:120978
Pan L, Zhou T, Lü L, Hu CK (2016) Predicting missing links and identifying spurious links via likelihood analysis. Sci Rep 6:22955
Pujari M, Kanawati R (2015) Link prediction in multiplex networks. Netw Hetero Med 10(1):17
Qiu J, et al (2019) NetSMF: Large-scale network embedding as sparse matrix factorization. In: proceedings of the world wide Web conference (ACM Press) 1509–1520
Ratha Pech et al (2019) Link prediction via linear optimization. Phys A: Stat Mech Appl 528:121319
Roberto Interdonato et al (2020) Multilayer network simplification: approaches, models and methods. Comput Sci Rev 36:100246
Samei Z, Jalili M (2019) Application of hyperbolic geometry in link prediction of multiplex networks. Sci Rep 9(1):1–11
Sen A, et al (2014) Identification of \(k\) most vulnerable nodes in multi-layered network using a new model of interdependency. In: 2014 IEEE conference on computer communications workshops (INFOCOM WKSHPS) 831-836
Tang Fengqin et al (2022) Link prediction for multilayer networks using interlayer structural information. Inter J Modern Phys C 33(01):2250003
Varshney LR et al (2011) Structural properties of the Caenorhabditis elegans neuronal network. PLoS Comput Biol 7(2):e1001066
Von Luxburg U (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416
Yang Y, et al (2012) Predicting links in multi-relational and heterogeneous networks. In: IEEE 12th international conference on data mining 755–764
Yao Y et al (2017) Link prediction via layer relevance of multiplex networks. Int J Modern Phys C 28(08):1750101
Yasami Y, Safaei F (2018) A novel multilayer model for missing link prediction and future link forecasting in dynamic complex networks. Phys A: Stat Mech Appl 492:2166–2197
Zhang Y, Levina E, Zhu J (2015) Estimating network edge probabilities by neighbourhood smoothing. Biometrika 104(4):771–783
Acknowledgements
The authors also thank Professor Bingyi Jing for discussions related to this paper. The project was sponsored by National Natural Science Foundation of China (12201235, 11971214), Natural Science Foundation of Anhui Province (2108085QA14) and the Excellent Young Talents Fund Program of Higher Education Institutions of Anhui Province (gxyqZD2022044).
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Tang, F., Li, C., Wang, C. et al. A comprehensive framework for link prediction in multiplex networks. Comput Stat 39, 939–961 (2024). https://doi.org/10.1007/s00180-023-01334-8
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DOI: https://doi.org/10.1007/s00180-023-01334-8