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International Conference on Combinatorial Optimization and Applications

COCOA 2020: Combinatorial Optimization and Applications pp 230–241Cite as

Mixed-Case Community Detection Problem in Social Networks

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12577))

Abstract

The problem of detecting communities is one of the essential problems in the study of social networks. To devise the algorithms of community detection, one should first define high-quality communities. In fact, there are no agreed methods to measure the quality of the community. In this paper, we consider a novel objective function of this problem. Our goal is to maximize not only the average of the sum of edge weights within communities (i.e., average-case) but also the sum of edge weights within the minimum community (i.e., worst-case). To balance both the average-case and worst-case problems, we introduce a parameter into our objective function and call it the mixed-cased community detection problem. We devise several approximation algorithms for the worst-case, such as the Greedy, Semi-Sandwich Approximation, and Local Search algorithms. For the average-case, an efficient Terminal-based algorithm is proposed. We prove that the best solution between the average-case and worst-case problems still can provide an approximate guarantee for any mixed-case community detection problem.

This work is supported by National Science Foundation under Grant No. 1907472 and by the National Natural Science Foundation of China under Grants No. 11991022 and No. 12071459.

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References

  1. Abbe, E.: Community detection and stochastic block models: recent developments. J. Mach. Learn. Res. 18(1), 6446–6531 (2017)

    MathSciNet  Google Scholar 

  2. Buchbinder, N., Schwartz, R., Weizman, B.: Simplex transformations and the multiway cut problem. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2400–2410. SIAM (2017)

    Google Scholar 

  3. Călinescu, G., Karloff, H., Rabani, Y.: An improved approximation algorithm for multiway cut. In: Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing, pp. 48–52 (1998)

    Google Scholar 

  4. Chakraborty, T., Ghosh, S., Park, N.: Ensemble-based overlapping community detection using disjoint community structures. Knowl.-Based Syst. 163, 241–251 (2019)

    Article  Google Scholar 

  5. Chekuri, C., Ene, A.: Approximation algorithms for submodular multiway partition. In: 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pp. 807–816. IEEE (2011)

    Google Scholar 

  6. Dahlhaus, E., Johnson, D.S., Papadimitriou, C.H., Seymour, P.D., Yannakakis, M.: The complexity of multiway cuts. In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing, pp. 241–251 (1992)

    Google Scholar 

  7. De Bacco, C., Power, E.A., Larremore, D.B., Moore, C.: Community detection, link prediction, and layer interdependence in multilayer networks. Phys. Rev. E 95(4), 042317 (2017)

    Article  Google Scholar 

  8. Fortunato, S., Hric, D.: Community detection in networks: a user guide. Phys. Rep. 659, 1–44 (2016)

    Article  MathSciNet  Google Scholar 

  9. Goldschmidt, O., Hochbaum, D.S.: A polynomial algorithm for the k-cut problem for fixed k. Math. Oper. Res. 19(1), 24–37 (1994)

    Article  MathSciNet  Google Scholar 

  10. Hagen, L., Kahng, A.B.: New spectral methods for ratio cut partitioning and clustering. IEEE Trans. Comput.-aided Des. Integr. Circ. Syst. 11(9), 1074–1085 (1992)

    Article  Google Scholar 

  11. Kannan, R., Vempala, S., Vetta, A.: On clusterings: good, bad and spectral. J. ACM (JACM) 51(3), 497–515 (2004)

    Article  MathSciNet  Google Scholar 

  12. Kelley, S., Goldberg, M., Magdon-Ismail, M., Mertsalov, K., Wallace, A.: Defining and discovering communities in social networks. In: Thai, M., Pardalos, P. (eds.) Handbook of Optimization in Complex Networks, pp. 139–168. Springer, Heidelberg (2012). https://doi.org/10.1007/978-1-4614-0754-6_6

  13. Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, pp. 631–640 (2010)

    Google Scholar 

  14. Lu, W., Chen, W., Lakshmanan, L.V.: From competition to complementarity: comparative influence diffusion and maximization. Proc. VLDB Endow. 9(2), 60–71 (2015)

    Article  Google Scholar 

  15. Mancoridis, S., Mitchell, B.S., Rorres, C., Chen, Y., Gansner, E.R.: Using automatic clustering to produce high-level system organizations of source code. In: Proceedings of 6th International Workshop on Program Comprehension. IWPC 1998 (Cat. No. 98TB100242), pp. 45–52. IEEE (1998)

    Google Scholar 

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

    Article  Google Scholar 

  17. Taha, K.: Disjoint community detection in networks based on the relative association of members. IEEE Trans. Comput. Soc. Syst. 5(2), 493–507 (2018)

    Article  Google Scholar 

  18. Tong, G., Cui, L., Wu, W., Liu, C., Du, D.Z.: Terminal-set-enhanced community detection in social networks. In: IEEE INFOCOM 2016-The 35th Annual IEEE International Conference on Computer Communications, pp. 1–9. IEEE (2016)

    Google Scholar 

  19. Von Luxburg, U.: A tutorial on spectral clustering. Stat. Comput. 17(4), 395–416 (2007)

    Article  MathSciNet  Google Scholar 

  20. Wei, K., Iyer, R.K., Wang, S., Bai, W., Bilmes, J.A.: Mixed robust/average submodular partitioning: fast algorithms, guarantees, and applications. In: Advances in Neural Information Processing Systems, pp. 2233–2241 (2015)

    Google Scholar 

  21. Weiss, R.S., Jacobson, E.: A method for the analysis of the structure of complex organizations. Am. Sociol. Rev. 20(6), 661–668 (1955)

    Article  Google Scholar 

  22. Xie, J., Kelley, S., Szymanski, B.K.: Overlapping community detection in networks: the state-of-the-art and comparative study. ACM Comput. Surv. (CSUR) 45(4), 1–35 (2013)

    Article  Google Scholar 

  23. Zeng, X., Wang, W., Chen, C., Yen, G.G.: A consensus community-based particle swarm optimization for dynamic community detection. IEEE Trans. Cybern. 50(6), 2502–2513 (2019)

    Article  Google Scholar 

  24. Zhe, C., Sun, A., Xiao, X.: Community detection on large complex attribute network. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2041–2049 (2019)

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yapu Zhang & Wenguo Yang

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX, 75080, USA

    Jianxiong Guo

Authors
  1. Yapu Zhang
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  2. Jianxiong Guo
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  3. Wenguo Yang
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Corresponding author

Correspondence to Wenguo Yang .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Xiamen University, Xiamen, China

    Zhongnan Zhang

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Zhang, Y., Guo, J., Yang, W. (2020). Mixed-Case Community Detection Problem in Social Networks. In: Wu, W., Zhang, Z. (eds) Combinatorial Optimization and Applications. COCOA 2020. Lecture Notes in Computer Science(), vol 12577. Springer, Cham. https://doi.org/10.1007/978-3-030-64843-5_16

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  • DOI: https://doi.org/10.1007/978-3-030-64843-5_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-64842-8

  • Online ISBN: 978-3-030-64843-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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