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GLEAM: a graph clustering framework based on potential game optimization for large-scale social networks

Abstract

With the growing explosion of online social networks, the study of large-scale graph clustering has attracted considerable interest. Most of traditional methods view the graph clustering problem as an optimization problem based on a given objective function; however, there are few methodical theories for the emergence of clusters over real-life networks. In this paper, each actor in online social networks is viewed as a selfish player in a non-cooperative game. The strategy associated with each node is defined as the cluster membership vector, and each one’s incentive is to maximize its own social identity by adopting the most suitable strategy. The definition of utility function in our game model is inspired by the conformity psychology, which is defined as the weighted average of one’s social identity by participating different clusters. With this setting, the proposed game can well match a potential game. So that the cluster could be shaped by the actions of those closely interactive users who adopt the same strategy in a Nash equilibrium. To this end, we propose a novel Graph cLustering framework based on potEntial gAme optiMization (GLEAM) for parallel graph clustering. It first utilize the cosine similarity to weight each edge in the original network. Then, an initial partition, including a number of clusters dominated by those potential “leader nodes”, is created by a fast heuristic process. Third, a potential game-based weighted Modularity optimization is used to improve the initial partition. Finally, we introduce the notion of potentially attractive cluster, and then discover the overlapping partition of the graph using a simple double-threshold procedure. Three phases in GLEAM are carefully designed for parallel execution. Experiments on real-world networks analyze the convergence inside GLEAM, and demonstrate the high performance of GLEAM by comparing it with the state-of-the-art community detection approaches in the literature.

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Notes

  1. http://snap.stanford.edu/data/.

  2. http://jselab.njue.edu.cn/teachers/Buzhan.html.

References

  1. Ahn YY, Bagrow JP, Lehmann S (2010) Link communities reveal multiscale complexity in networks. Nature 466(7307):761–764

    Article  Google Scholar 

  2. Alvari H, Hashemi S, Hamzeh A (2012) Detecting overlapping communities in social networks by game theory and structural equivalence concept. In: Lei J, Wang FL, Deng H, Miao D (eds) The 4th international conference on artificial intelligence and computational intelligence. Chengdu, China, pp 620–630

  3. Basu S, Maulik U (2015) Community detection based on strong Nash stable graph partition. Soc Netw Anal Min 5(1):1–15

    Article  Google Scholar 

  4. Berry JW, Hendrickson B, LaViolette RA et al (2011) Tolerating the community detection resolution limit with edge weighting. Phys Rev E 83(5):056119

    Article  Google Scholar 

  5. Blondel VD, Guillaume JL, Lambiotte R et al (2008) (2008) Fast unfolding of communities in large networks. J Stat Mech Theor Exp 10:P10008

    Article  Google Scholar 

  6. Bu Z, Wu Z, Cao J et al (2016) Local community mining on distributed and dynamic networks from a multiagent perspective. IEEE Trans Cybern 46(4):986–999

    Article  Google Scholar 

  7. Cao L, Li X, Han L (2013) Detecting community structure of networks using evolutionary coordination games. In: Chen CW, Cao W, Vandewalle J (eds) The 21th international conference on pattern recognition. Beijing, China, pp 2533–2536

  8. Chen W, Liu Z, Sun X et al (2011) Community detection in social networks through community formation games. In: Proceedings of the 22th international joint conference on artificial intelligence, Barcelona, Spain, July 2011, pp 2576–2581

  9. Cialdini RB, Goldstein NJ (2004) Social influence: compliance and conformity. Annu Rev Psychol 55:591–621

    Article  Google Scholar 

  10. Costa H, Merschmann LHC, Barth F et al (2014) Pollution, bad-mouthing, and local marketing: the underground of location-based social networks. Inf Sci 279:123–137

    Article  Google Scholar 

  11. Danon L, Diazguilera A, Duch J et al (2005) Comparing community structure identification . J Stat Mech Theor Exp 2005(09):P09008

  12. Evans TS, Lambiotte R (2010) Line graphs of weighted networks for overlapping communities. Eur Phys J B 77(2):265–272

    Article  Google Scholar 

  13. Farkas I, Abel D, Palla G et al (2007) Weighted network modules. New J Phys 9(6):180

    Article  Google Scholar 

  14. Fortunato S, Barthlemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci 104(1):36–41

    Article  Google Scholar 

  15. Fortunato S (2010) Community detection in graphs. Phys Rep 486(3):75–174

    Article  MathSciNet  Google Scholar 

  16. Gong M, Cai Q, Chen X et al (2014) Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition. IEEE Trans Evol Comput 18(1):82–97

    Article  Google Scholar 

  17. Gregory S (2009) Finding overlapping communities in networks by label propagation. New J Phys 12(10):2011–2024

    Google Scholar 

  18. Hajibagheri A, Alvari H, Hamzeh A et al (2012) Social networks community detection using the shapley value. In: The 16th CSI international symposium on artificial intelligence and signal processing, Shiraz, Fars, Iran, May 2012, pp 222–227

  19. Hofman JM, Wiggins CH (2008) Bayesian approach to network modularity. Phys Rev Lett 100(25):258701

    Article  Google Scholar 

  20. Jiang F, Xu J (2015) Dynamic community detection based on game theory in social networks. In: 2015 IEEE international conference on big data, Santa Clara, CA, USA, October 2015, pp 2368–2373

  21. Jonnalagadda A, Kuppusamy L (2016) A survey on game theoretic models for community detection in social networks. Soc Netw Anal Min 6(1):1–24

    Article  Google Scholar 

  22. Kim Y, Jeong H (2011) Map equation for link communities. Phys Rev E 84(2):026110

    Article  MathSciNet  Google Scholar 

  23. Kumpula JM, Kivela M, Kaski K et al (2008) Sequential algorithm for fast clique percolation. Phys Rev E 78(2):026109

    Article  Google Scholar 

  24. Lancichinetti A, Fortunato S, Kertsz J (2009) Detecting the overlapping and hierarchical community structure of complex networks. New J Phys 11(3):19–44

    Article  Google Scholar 

  25. Lancichinetti A, Fortunato S (2009) Community detection algorithms: a comparative analysis. Phys Rev E 80(5):056117

    Article  Google Scholar 

  26. Lancichinetti A, Radicchi F, Ramasco JJ et al (2011) Finding statistically significant communities in networks. Plos One 6(4):e18961

    Article  Google Scholar 

  27. Lee C, McDaid A, Reid F et al (2010) Detecting highly overlapping community structure by greedy clique expansion. In: The 4th SNA-KDD Workshop, Washington DC, July 2010

  28. Li HJ, Bu Z, Li A (2016) Fast and accurate mining the community structure: integrating center locating and membership optimization. IEEE Trans Knowl Data Eng 28(9):2349–2362

    Article  Google Scholar 

  29. Long B, Zhang ZF, Yu PS (2010) A general framework for relation graph clustering. Knowl Inf Syst 24(3):393–413

    Article  Google Scholar 

  30. Mcsweeney PJ, Mehrotra K, Oh JC (2014) A game theoretic framework for community detection. In: 2014 IEEE/ACM international conference on advances in social networks analysis and mining, Beijing, China, August 2014, pp 227–234

  31. Narayanam R, Narahari Y (2012) A game theory inspired, decentralized, local information based algorithm for community detection in social graphs. The 21th international conference on pattern recognition, Tsukuba Science City, Japan, November 2012, pp 1072–1075

  32. Newman ME (2004) Analysis of weighted networks. Phys Rev E 70(5):056131

    Article  Google Scholar 

  33. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026113

    Article  Google Scholar 

  34. Palla G, Derenyi I, Farkas I et al (2005) Uncovering the overlapping community structure of complex networks in nature and society. Nature 435:814–818

    Article  Google Scholar 

  35. Pons P, Latapy M (2005) Computing communities in large networks using random walks. Int Symp Comput Inf Sci 3733(2):284–293

    MATH  Google Scholar 

  36. Prat-Perez A, Dominguez-Sal D, Larriba-Pey JL (2014) High quality, scalable and parallel community detection for large real graphs. In: Broder AZ, Shim K, Suel T (eds) Proceedings of the 23rd international conference on World wide web, Seoul, Republic of Korea, April 2014, pp 225–236

  37. Raghavan UN, Albert R, Kumara S (2007) Near linear time algorithm to detect community structures in large-scale networks. Phys Rev E 76(2):036106

    Article  Google Scholar 

  38. Reichardt J, Bornholdt S (2006) Statistical mechanics of community detection. Phys Rev E 74(2):016110

    Article  MathSciNet  Google Scholar 

  39. Rosvall M, Bergstrom CT (2008) Maps of random walks on complex networks reveal community structure. Proc Natl Acad Sci 105(4):1118–1123

    Article  Google Scholar 

  40. Schaeffer SE (2007) Survey: graph clustering. Comput Sci Rev 1(1):27–64

    Article  MATH  Google Scholar 

  41. Shen H, Cheng X, Cai K et al (2009) Detect overlapping and hierarchical community structure in networks. Phys A Stat Mech Appl 388(8):1706–1712

    Article  Google Scholar 

  42. Souam F, Aitelhadj A, Baba-Ali R (2014) Dual modularity optimization for detecting overlapping communities in bipartite networks. Knowl Inf Syst 40(2):455–488

    Article  Google Scholar 

  43. Szczepański PH, Barcz AS, Michalak TP, et al (2015) The game-theoretic interaction index on social networks with applications to link prediction and community detection. In: Proceedings of the 24th international joint conference on artificial intelligence Buenos Aires, Argentina, July 2015, pp 638–644

  44. Tsuji R (2002) Interpersonal influence and attitude change toward conformity in small groups: a social psychological model. J Math Sociol 26(1–2):17–34

    Article  MATH  Google Scholar 

  45. Udrescu L, Sbarcea L, Topirceanu A et al (2016) Clustering drug-drug interaction networks with energy model layouts: community analysis and drug repurposing. Sci Rep 6:32745

    Article  Google Scholar 

  46. Xie J, Szymanski BK (2012) Towards linear time overlapping community detection in social networks. In: Tan PN, Chawla S, Ho CK, Bailey J (eds) The 16th Pacific-Asia conference on knowledge discovery and data mining, Malaysia, September 2012, pp 25–36

  47. Xie J, Kelley S, Szymanski BK (2013) Overlapping community detection in networks: the state-of-the-art and comparative study. ACM Comput Surv 45(4):43

    Article  MATH  Google Scholar 

  48. Yang J, Leskovec J (2013) Overlapping community detection at scale: a nonnegative matrix factorization approach. In: Ferragina P, Gionis A (eds) Proceedings of the 6th ACM international conference on web search and data mining, Rome, Italy, February 2013, pp 587–596

  49. Zhou L, Lv K, Yang P et al (2015) An approach for overlapping and hierarchical community detection in social networks based on coalition formation game theory. Exp Syst Appl 42(24):9634–9646

    Article  Google Scholar 

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Acknowledgements

This research was partially supported by National Key Research and Development Program of China under Grant 2016YFB1000901; National Natural Science Foundation of China under Grant 61502222 and 71401194; Natural Science Foundation of Jiangsu Province of China under Grant BK20150988; Key Program of National Natural Science Foundation of China under Grant 91646204; National Science and Technology Pillar Program of Jiangsu Province of China under Grant BE2016178; and Young Elite Teacher Project of Central University of Finance and Economics under Grants QYP1603.

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Bu, Z., Cao, J., Li, HJ. et al. GLEAM: a graph clustering framework based on potential game optimization for large-scale social networks. Knowl Inf Syst 55, 741–770 (2018). https://doi.org/10.1007/s10115-017-1105-6

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  • DOI: https://doi.org/10.1007/s10115-017-1105-6

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