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A link prediction algorithm based on low-rank matrix completion

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Abstract

Link prediction is an essential research area in network analysis. Based on the technique of matrix completion, an algorithm for link prediction in networks is proposed. We propose a new model to describe matrix completion. In addition to the observed data, the model takes the noise matrix into account, which is important for detecting missing links. We propose an alternative iteration algorithm to solve matrix completion. The algorithm uses the proximal forward-backward splitting to minimize the nuclear and L2,1 norm simultaneously. A random projected shrinkage operator on the singular values is defined, and an algorithm for implementing the projected shrinkage operator is presented. Using this operator, the time complexity of our algorithm is reduced greatly and reaches the lower bound of the time complexity for a similarity-based link prediction method. The empirical results of real-world networks show that the proposed algorithm can achieve higher quality prediction results than other algorithms.

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References

  1. Zhang Z, Wen J, Sun L, Deng Q, Su S, Yao P (2017) Efficient incremental dynamic link prediction algorithms in social network. Knowl-Based Syst 132:226–235

    Article  Google Scholar 

  2. Rahman MS, Dey LR, Haider S, Uddin MA, Islam M (2017) Link prediction by correlation on social network. In: 2017 20th international conference of computer and information technology (ICCIT), pp 1–6

  3. Tuninetti M, Tamea S, Laio F, Ridolfi L (2017) To trade or not to trade: link prediction in the virtual water network. Adv Water Resour 110:528–537

    Article  Google Scholar 

  4. Fan C, Liu Z, Lu X, Xiu B, Chen Q (2017) An efficient link prediction index for complex military organization. Physica A: Stat Mech Appl 469(1):572–587

    Article  Google Scholar 

  5. Li J, Ge B, Yang K, Chen Y, Tan Y (2017) Meta-path based heterogeneous combat network link prediction. Physica A: Stat Mech Appl 482:507–523

    Article  MathSciNet  Google Scholar 

  6. Ahmed NM, Chen L, Wang Y, Li B, Li Y, Liu W (2018) DeepEye: link prediction in dynamic networks based on non-negative matrix factorization. Big Data Mining Anal 1(1):19–33

    Article  Google Scholar 

  7. Moradabadi B, Meybodi MR (2018) Link prediction in weighted social networks using learning automata. Eng Appl Artif Intell 70:16–24

    Article  Google Scholar 

  8. Kaya B, Poyraz M (2015) Age-series based link prediction in evolving disease networks. Comput Biol Med 63:1–10

    Article  Google Scholar 

  9. Guimera R, Sales-Pardo M (2010) Missing and spurious interactions and the reconstruction of complex networks. Proc Natl Acad Sci 106(52):22073–22078

    Article  Google Scholar 

  10. Talasu N, Jonnalagadda A, Pillai SSA, Rahul J (2017) A link prediction based approach for recommendation systems. In: 2017 international conference on advances in computing, communications and informatics (ICACCI), pp 2059–2062

  11. Sun Z, Peng Q, Lv J et al (2016) A prediction model of post subjects based on information lifecycle in forum. Inf Sci 337–338:59–71

    Article  Google Scholar 

  12. Klimek P, Jovanovic AS, Egloff R, Schneider R (2016) Successful fish go with the flow: citation impact prediction based on centrality measures for term–document networks. Scientometrics 107(3):1265–1282

    Article  Google Scholar 

  13. Kaya B, Poyraz M (2016) Unsupervised link prediction in evolving abnormal medical parameter networks. Int J Mach Learn Cybern 7(1):145–155

    Article  Google Scholar 

  14. Ge MQ, Li A, Wang MH (2016) A bipartite network-based method for prediction of long non-coding RNA–protein interactions. Genomics Proteomics Bioinf 14(1):62–71

    Article  Google Scholar 

  15. Fang L, Fang H, Tian Y, Yang T, Zhao J (2017) The alliance relationship analysis of international terrorist organizations with link prediction. Physica A: Stat Mech Appl 482:573–584

    Article  Google Scholar 

  16. Zhang J (2017) Uncovering mechanisms of co-authorship evolution by multirelations-based link prediction. Inf Process Manag 53(1):42

    Article  Google Scholar 

  17. Sharma PK, Rathore S, Park JH (2017) Multilevel learning based modeling for link prediction and users’ consumption preference in Online Social Networks. Futur Gener Comput Syst. Available online 25 August

  18. Kaya B, Poyraz M (2014) Supervised link prediction in symptom networks with evolving case. Measurement 56:231–238

    Article  Google Scholar 

  19. Ma X, Liao JL, Djouadi SM, Cao Q (2014) LIPS: link prediction as a service for data aggregation applications. Ad Hoc Netw 19:43–58

    Article  Google Scholar 

  20. Aiello LM, Barrat A, Schifanella R et al (2012) Friendship prediction and homophily in social media. ACM Trans Web (TWEB) 6(2):9

    Google Scholar 

  21. Zhang P, Qiu D, Zeng A, Xiao J (2018) A comprehensive comparison of network similarities for link prediction and spurious link elimination. Physica A: Stat Mech Appl 500:97–105

    Article  MathSciNet  Google Scholar 

  22. Shakibian H, Charakri NM (2018) Statistical similarity measures for link prediction in heterogeneous complex networks. Physica A: Stat Mech Appl. Available online 23

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

    Article  Google Scholar 

  24. Wang XJ, Zhang X, Zhao CL et al (2015) Predicting link directions using local directed path. Physica A: Stat Mech Appl 419:260–267

    Article  Google Scholar 

  25. Sarma AD, Molla AR, Pandurangan G (2015) Distributed computation in dynamic networks via random walks. Theor Comput Sci 58(1):45–66

    Article  MathSciNet  Google Scholar 

  26. Liu WP, Lü L (2010) Link prediction based on local random walk. Eur Phys Lett 89(5):58007

    Article  Google Scholar 

  27. Hu FY, Wong HS (2013) Labeling of human motion based on CBGA and probabilistic model. Int J Smart Sens Intell Syst 6(2):583–609

    Google Scholar 

  28. Barbieri N, Bonchi F, Manco G (2014) Who to follow and why: link prediction with explanations. In: Proceedings of the 20th ACM SIGKDD international conference on knowledge discovery and data mining, pp 1266–1275

  29. Gao S, Denoyer L, Gallinari P (2011) Temporal link prediction by integrating content and structure information. In: Proceedings of CIKM’11, pp 1169–1174

  30. Zeng ZZ, Chen K-J, Zhang S, Zhang H (2013) A link prediction approach using semi-supervised learning in dynamic networks. In: Proceedings of sixth international conference on advanced computational intelligence (ICACI), pp 276–280

  31. Vu DQ, Asuncion AU, Hunter DR, Smyth P (2011) Continuous-time regression models for longitudinal networks. In: Advances in neural information processing systems 24: proceedings of the 25th annual conference on neural information processing systems, pp 1–9

  32. Pujari M, Kanawati R (2012) Supervised rank aggregation approach for link prediction in complex networks. In: WWW 2012 companion, pp 1189–1196

  33. Bao ZF, Zeng Y, Tay YC (2013) sonL: social network link prediction by principal component regression. In: Proceedings of the 2013 IEEE/ACM international conference on advances in social networks analysis and mining

  34. He YL, Liu JNK, Hu Y-X, Wang X-Z (2015) OWA operator based link prediction ensemble for social network. Expert Syst Appl 42(1):21–50

    Article  Google Scholar 

  35. Bliss CA, Frank MR, Danforth CM, Dodds PS (2014) An evolutionary algorithm approach to link prediction in dynamic social networks. J Comput Sci 5(5):750–764

    Article  MathSciNet  Google Scholar 

  36. Sherkat E, Rahgozar M, Asadpour M (2015) Structural link prediction based on ant colony approach in social networks. Physica A: Stat Mech Appl 419(1):80–94

    Article  Google Scholar 

  37. Chen BL, Chen L, Li B (2016) A fast algorithm for predicting links to nodes of interest. Inf Sci 329:552–567

    Article  Google Scholar 

  38. Ding J, Jiao L, Wu J, Liu F (2016) Prediction of missing links based on community relevance and ruler inference. Knowl-Based Syst 98:200–215

    Article  Google Scholar 

  39. Wu Z, Lin Y, Zhao Y, Yan H (2018) Improving local clustering based top-L link prediction methods via asymmetric link clustering information. Physica A: Stat Mech Appl 492:1859–1874

    Article  Google Scholar 

  40. Dong E, Li J, Xie Z (2014) Link prediction via convex nonnegative matrix factorization on multiscale blocks. J Appl Math 2014 :1–9

    MathSciNet  Google Scholar 

  41. Dai C, Chen L, Li B, Li Y (2017) Link prediction in multi-relational networks based on relational similarity. Inf Sci 394–395:198–216

    Article  Google Scholar 

  42. Song G, Dai Q (2017) A novel double deep ELMs ensemble system for time series forecasting. Knowl-Based Syst 134:31–49

    Article  Google Scholar 

  43. Han X, Dai Q (2018) Batch-normalized Mlpconv-wise supervised pre-training network in network. Appl Intell 48(1):142–155

    Article  Google Scholar 

  44. Zhang M, Cui Z, Neumann M, Chen Y (2018) An end-to-end deep learning architecture for graph classification. In: Proceedings of association for the advancement of artificial intelligence (AAAI-18)

  45. Zhang M, Chen Y (2017) Weisfeiler-Lehman neural machine for link prediction. In: Proceedings of ACM SIGKDD conference on knowledge discovery and data mining (KDD-17) oral presentation

  46. Ratha P et al (2017) Link prediction via matrix completion. EPL (Europhys Lett) 117(3):38002

    Article  Google Scholar 

  47. Mohtashemi B, Ketseoglou T (2016) Log-normal matrix completion for large scale link prediction arXiv:1601.07714v1 [cs.SI]

  48. Candes EJ, Tao T (2010) The power of convex relaxation: near-optimal matrix completion. IEEE Trans Inf Theory 56(5):2053–2080

    Article  MathSciNet  Google Scholar 

  49. Recht B, Fazel M, Parrilo PA (2010) Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev 52(3):471–501

    Article  MathSciNet  Google Scholar 

  50. Cai T, Zhou WX (2013) A max-norm constrained minimization approach to 1-bit matrix completion. J Mach Learn Res 14(1):3619–3647

    MathSciNet  MATH  Google Scholar 

  51. Cai JF, Candes EJ, Shen ZW (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982

    Article  MathSciNet  Google Scholar 

  52. Jain P, Meka R, Dhillon IS (2010) Guaranteed rank minimization via singular value projection. In: NIPS, pp 937–945

  53. Keshavan RH, Montanari A, Oh S (2010) Matrix completion from a few entries. IEEE Trans Inf Theory 56(6):2980–2998

    Article  MathSciNet  Google Scholar 

  54. Shen J, Xu H, Li P (2014) Online optimization for max-norm regularization. In: NIPS, pp 1718–1726

  55. Huang J, Nie FP, Huang H, Tu YC, Lei Y (2013) Social trust prediction using multi-relational networks. ACM Trans Knowl Discov Data 7(4):17

    Article  Google Scholar 

  56. Wang YX, Xu H (2012) Stability of matrix factorization for collaborative filtering. In: ICML

  57. Srebro N, Shraibman A (2005) Rank, trace-norm and max-norm. In: Learning theory, pp 545–560

    Chapter  Google Scholar 

  58. Salakhutdinov R, Srebro N (2010) Collaborative filtering in a non-uniform world: learning with the weighted trace norm. tc (X) 10:2

    Google Scholar 

  59. Candès EJ, Recht B (2009) Exact matrix completion via convex optimization. Found Comput Math 9 (6):717–727

    Article  MathSciNet  Google Scholar 

  60. Combettes PL, Wajs VR (2005) Signal recivery by proximal forward-backward splitting. Multiscale Model Simul 4(4):1168–1200

    Article  MathSciNet  Google Scholar 

  61. Liu G, Lin Z, Yan S et al (2013) Robust recovery of subspace structure by low rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171–184

    Article  Google Scholar 

  62. Ma S, Goldfarb D, Chen LF (2011) Fixed point and Bregman iterative methods for matrix rank minimization. Math Program 128(1):321–353

    Article  MathSciNet  Google Scholar 

  63. Netflix Inc Netfilx Prize. http://www.netflixprize.com/. Accessed in March, 2017

  64. GroupLens MovieLens 100K Datase, https://grouplens.org/datasets/movielens/100k/. Accessed in March, 2017

  65. Chen L, Zheng J, Gao M, Zhou A, Zeng W, Chen H (2017) TLRec: transfer learning for cross-domain recommendation. In: International conference on big knowledge. IEEE, pp 167–172

  66. Gao T, Zhang Y, Zhu X, Li L (2017) Personalized recommendation based on unbalanced symmetrical mass diffusion. In: 2017 IEEE third international conference on multimedia big data, pp 384–388

  67. Leskovec J (2017) Stanford large network dataset collection, http://snap.stanford.edu/data/, accessed in March

  68. The DBLP Team, Computer Science Biliography. https://dblp.uni-trier.de/. Accessed: March 2017

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Acknowledgements

This research was supported in part by the Chinese National Natural Science Foundation under grant Nos. 61379066, 61472344, 6161154037, 61070047, 61379064, 61402395, and 61602202; Natural Science Foundation of Jiangsu Province under contracts BK20130452, BK2012672, BK2012128, BK20140492 and Natural Science Foundation of Education Department of Jiangsu Province under contract 12KJB520019, 13KJB520026, 09KJB20013. Six talent peaks project in Jiangsu Province(Grant No. 2011-DZXX-032).

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Authors and Affiliations

  1. Department of Computer Science, Yangzhou University, Yangzhou, 225127, China

    Man Gao, Ling Chen, Bin Li & Wei Liu

  2. State Key Lab of Novel Software Tech, Nanjing University, Nanjing, 210093, China

    Ling Chen & Bin Li

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  1. Man Gao
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  2. Ling Chen
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  4. Wei Liu
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Correspondence to Ling Chen.

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Gao, M., Chen, L., Li, B. et al. A link prediction algorithm based on low-rank matrix completion. Appl Intell 48, 4531–4550 (2018). https://doi.org/10.1007/s10489-018-1220-4

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