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Multiresolution community detection in complex networks by using a decomposition based multiobjective memetic algorithm

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Abstract

Community structures are sets of nodes that are densely linked with each other, reflecting the functional modules of real-world systems. Most classical works for community detection (CD) are based on the optimization of an objective function, namely modularity. However, it has been recently demonstrated that there exists a resolution limit in the modularity optimization based CD methods, i.e., the communities cannot be detected if their scales are smaller than a certain threshold. To overcome this resolution limit, in this paper, we propose a decomposition based multiobjective memetic algorithm (called MDMCD) for multiresolution CD (MCD) in complex networks, aiming to detect communities at multiple resolution levels. MDMCD first models the MCD problem as a multiobjective optimization problem (MOP) with two contradictory objectives, namely the intra-link ratio and inter-link ratio. Then, it devises a multiobjective memetic optimization framework that combines a decomposition based multiobjective evolutionary algorithm with a two-level local search to solve the modeled MOP. In this framework, the modeled MOP is first decomposed into a set of single-objective optimization subproblems, each of which corresponds to a CD problem in a certain resolution level. Subsequently, these subproblems are simultaneously optimized by the evolutionary operators and the local search, taking the network-specific knowledge into consideration. Finally, MDMCD returns a population of solutions in a single simulation run, reflecting the community divisions at multiple resolution levels. Experiments on both the simulated and real-world networks show the effectiveness of MDMCD in detecting multiresolution community structures.

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Data availibility

The datasets analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Arenas A, Diaz-Guilera A, Pérez-Vicente CJ (2006) Synchronization reveals topological scales in complex networks. Phys Rev Lett 96(11):114,102

    Article  Google Scholar 

  2. Blondel VD, Guillaume JL, Lambiotte R et al (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp 10:P10,008

    Article  MATH  Google Scholar 

  3. Chen D, Zou F, Lu R et al (2016) Multi-objective optimization of community detection using discrete teaching-learning-based optimization with decomposition. Inf Sci 369:402–418

    Article  MathSciNet  Google Scholar 

  4. Chen X, Ong YS, Lim MH et al (2011) A multi-facet survey on memetic computation. IEEE Trans Evol Comput 15(5):591–607

    Article  Google Scholar 

  5. Cheng F, Cui T, Su Y et al (2018) A local information based multi-objective evolutionary algorithm for community detection in complex networks. Appl Soft Comput 69:357–367

    Article  Google Scholar 

  6. Clauset A, Newman ME, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70(6):066,111

    Article  Google Scholar 

  7. Clauset A, Moore C, Newman ME (2008) Hierarchical structure and the prediction of missing links in networks. Nature 453(7191):98–101

    Article  Google Scholar 

  8. Deb K, Pratap A, Agarwal S et al (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  9. Fortunato S (2010) Community detection in graphs. Phys Rep 486(3–5):75–174

    Article  MathSciNet  Google Scholar 

  10. Fortunato S, Barthelemy M (2007) Resolution limit in community detection. Proceedings of the Aational Academy of Sciences 104(1):36–41

    Article  Google Scholar 

  11. Girvan M, Newman ME (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99(12):7821–7826

    Article  MathSciNet  MATH  Google Scholar 

  12. Gong M, Jiao L, Du H et al (2008) Multiobjective immune algorithm with nondominated neighbor-based selection. Evol Comput 16(2):225–255

    Article  Google Scholar 

  13. Gong M, Fu B, Jiao L et al (2011) Memetic algorithm for community detection in networks. Phys Rev E 84(5):056,101

    Article  Google Scholar 

  14. Gong M, Ma L, Zhang Q et al (2012) Community detection in networks by using multiobjective evolutionary algorithm with decomposition. Phys A 391(15):4050–4060

    Article  Google Scholar 

  15. Gong M, Chen X, Ma L et al (2013) Identification of multi-resolution network structures with multi-objective immune algorithm. Appl Soft Comput 13(4):1705–1717

    Article  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. Gong M, Cai Q, Ma L et al (2017) Computational intelligence for network structure analytics. Springer

  18. Gu F, Liu HL, Tan KC (2012) A multiobjective evolutionary algorithm using dynamic weight design method. Int J Innov Comput Inf Control 8(5B):3677–3688

    Google Scholar 

  19. He X, Zhou Y, Chen Z et al (2018) Evolutionary many-objective optimization based on dynamical decomposition. IEEE Trans Evol Comput 23(3):361–375

    Article  Google Scholar 

  20. Hu L, Zhang J, Pan X et al (2021) An effective link-based clustering algorithm for detecting overlapping protein complexes in protein-protein interaction networks. IEEE Trans Netw Sci Eng. https://doi.org/10.1109/TNSE.2021.3109880

    Article  Google Scholar 

  21. Huang J, Sun H, Song Q et al (2012) Revealing density-based clustering structure from the core-connected tree of a network. IEEE Trans Knowl Data Eng 25(8):1876–1889

    Article  Google Scholar 

  22. Jeub LG, Sporns O, Fortunato S (2018) Multiresolution consensus clustering in networks. Sci Rep 8(1):1–16

    Article  Google Scholar 

  23. Jin D, Li R, Xu J (2019) Multiscale community detection in functional brain networks constructed using dynamic time warping. IEEE Trans Neural Syst Rehabil Eng 28(1):52–61

    Article  Google Scholar 

  24. Kumpula JM, Saramäki J, Kaski K et al (2007) Limited resolution in complex network community detection with potts model approach. Eur Phys J B 56(1):41–45

    Article  Google Scholar 

  25. Lancichinetti A, Fortunato S (2011) Limits of modularity maximization in community detection. Phys Rev E 84(6):066,122

    Article  Google Scholar 

  26. Lancichinetti A, Fortunato S, Kertész J (2009) Detecting the overlapping and hierarchical community structure in complex networks. NewJ Phys 11(3):033,015

    Article  Google Scholar 

  27. Li D, Wang C, Zhang S et al (2017) Positive influence maximization in signed social networks based on simulated annealing. Neurocomputing 260:69–78

    Article  Google Scholar 

  28. Li G, Zhu Z, Ma L et al (2021) Multi-objective memetic algorithm for core-periphery structure detection in complex network. Memetic Comput 13(3):285–306

    Article  Google Scholar 

  29. Li M, Lu S, Zhang L et al (2021) A community detection method for social network based on community embedding. IEEE Trans Comput Soc Syst 8(2):308–318

    Article  Google Scholar 

  30. Li Z, Zhang S, Wang RS et al (2008) Quantitative function for community detection. Phys Rev E 77(3):036109

    Article  Google Scholar 

  31. Li Z, Liu J, Wu K (2018) A multiobjective evolutionary algorithm based on structural and attribute similarities for community detection in attributed networks. IEEE Trans Cybern 48(7):1963–1976

    Article  Google Scholar 

  32. Liu X, Du Y, Jiang M et al (2020) Multiobjective particle swarm optimization based on network embedding for complex network community detection. IEEE Trans Comput Soc Syst 7(2):437–449

    Article  Google Scholar 

  33. Luo W, Zhang D, Ni L et al (2021) Multiscale local community detection in social networks. IEEE Trans Knowl Data Eng 33(3):1102–1112

    Google Scholar 

  34. Lyu C, Shi Y, Sun L (2021) A novel local community detection method using evolutionary computation. IEEE Trans Cybern 51(6):3348–3360

    Article  Google Scholar 

  35. Ma L (2015) structure and behavior analysis of complex networks based on heuristic evolutionary computation. PhD thesis, Xidian University

  36. Ma L, Gong M, Liu J et al (2014) Multi-level learning based memetic algorithm for community detection. Appl Soft Comput 19:121–133

    Article  Google Scholar 

  37. Ma L, Li J, Lin Q et al (2018) Reliable link inference for network data with community structures. IEEE Trans Cybern 49(9):3347–3361

    Article  Google Scholar 

  38. Ma L, Li J, Lin Q et al (2019) Cost-aware robust control of signed networks by using a memetic algorithm. IEEE Trans Cybern 50(10):4430–4443

    Article  Google Scholar 

  39. Ma L, Wang S, Lin Q et al (2020) Multi-neighborhood learning for global alignment in biological networks. IEEE/ACM Trans Comput Biol Bioinform. https://doi.org/10.1109/TCBB.2020.2985838

    Article  Google Scholar 

  40. Mei Y, Tang K, Yao X (2011) Decomposition-based memetic algorithm for multiobjective capacitated arc routing problem. IEEE Trans Evol Comput 15(2):151–165

    Article  Google Scholar 

  41. Newman ME (2006) Modularity and community structure in networks. Proc Natl Acad Sci 103(23):8577–8582

    Article  Google Scholar 

  42. Nguyen QH, Ong YS, Lim MH (2009) A probabilistic memetic framework. IEEE Trans Evol Comput 13(3):604–623

    Article  Google Scholar 

  43. Ong YS, Lim MH, Chen X (2010) Memetic computation-past, present & future [research frontier]. IEEE Comput Intell Mag 5(2):24–31

    Article  Google Scholar 

  44. Pizzuti C (2011) A multiobjective genetic algorithm to find communities in complex networks. IEEE Trans Evol Comput 16(3):418–430

    Article  Google Scholar 

  45. Pizzuti C (2018) Evolutionary computation for community detection in networks: a review. IEEE Trans Evol Comput 22(3):464–483

    Article  Google Scholar 

  46. Pons P, Latapy M (2011) Post-processing hierarchical community structures: quality improvements and multi-scale view. Theoret Comput Sci 412(8–10):892–900

    Article  MathSciNet  MATH  Google Scholar 

  47. Radicchi F, Castellano C, Cecconi F et al (2004) Defining and identifying communities in networks. Proc Aational Acad Sci 101(9):2658–2663

    Article  Google Scholar 

  48. 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 

  49. Shi C, Yan Z, Cai Y et al (2012) Multi-objective community detection in complex networks. Appl Soft Comput 12(2):850–859

    Article  Google Scholar 

  50. Shi J, Zhang Q, Sun J (2018) Ppls/d: parallel pareto local search based on decomposition. IEEE Trans Cybern 50(3):1060–1071

    Article  Google Scholar 

  51. Sindhya K, Sinha A, Deb K, et al (2009) Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems. In: 2009 IEEE congress on evolutionary computation, IEEE, pp 2919–2926

  52. Su J, Havens TC (2014) Quadratic program-based modularity maximization for fuzzy community detection in social networks. IEEE Trans Fuzzy Syst 23(5):1356–1371

    Article  Google Scholar 

  53. Su Y, Liu C, Niu Y et al (2021) A community structure enhancement-based community detection algorithm for complex networks. IEEE Trans Syst Man Cybern Syst 51(5):2833–2846

    Article  Google Scholar 

  54. Tang K, Mei Y, Yao X (2009) Memetic algorithm with extended neighborhood search for capacitated arc routing problems. IEEE Trans Evol Comput 13(5):1151–1166

    Article  Google Scholar 

  55. Wen X, Chen WN, Lin Y et al (2017) A maximal clique based multiobjective evolutionary algorithm for overlapping community detection. IEEE Trans Evol Comput 21(3):363–377

    Google Scholar 

  56. Wu H, Kuang L, Wang F et al (2017) A multiobjective box-covering algorithm for fractal modularity on complex networks. Appl Soft Comput 61:294–313

    Article  Google Scholar 

  57. Ying C, Liu J, Wu K et al (2021) A multiobjective evolutionary approach for solving large-scale network reconstruction problems via logistic principal component analysis. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2021.3109914

    Article  Google Scholar 

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

    Article  Google Scholar 

  59. Zhang L, Pan H, Su Y et al (2017) A mixed representation-based multiobjective evolutionary algorithm for overlapping community detection. IEEE Trans Cybern 47(9):2703–2716

    Article  Google Scholar 

  60. Zhang P, Moore C (2014) Scalable detection of statistically significant communities and hierarchies, using message passing for modularity. Proc Natl Acad Sci 111(51):18,144-18,149

    Article  Google Scholar 

  61. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731

    Article  Google Scholar 

  62. Zitzler E, Laumanns M, Thiele L (2001) Spea2: Improving the strength pareto evolutionary algorithm. TIK-Report 103

  63. Zou F, Chen D, Li S et al (2017) Community detection in complex networks: multi-objective discrete backtracking search optimization algorithm with decomposition. Appl Soft Comput 53:285–295

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the National Key R &D Program of China under Grant 2020YFA0908700, in part by the National Natural Science Foundation of China under Grants 62173236, 61803269, 61876110, 61806130, 61976142, U1713212, 62072315, 62176164, 61976142 and 61836005, in part by the Natural Science Foundation of Guangdong Province under Grant 2020A1515010790; and in part by the Technology Research Project of Shenzhen City under Grant JCYJ20190808174801673.

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Authors and Affiliations

  1. College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, 518060, China

    Zengyang Shao, Lijia Ma, Qiuzhen Lin & Jianqiang Li

  2. WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, Li Ka Shing Faculty of Medicine, The University of Hong Kong, Hong Kong, China

    Yuan Bai

  3. School of Electronic Engineering, The Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, Xidian University, Xi’an, 710071, China

    Shanfeng Wang

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  1. Zengyang Shao
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Correspondence to Lijia Ma.

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Shao, Z., Ma, L., Bai, Y. et al. Multiresolution community detection in complex networks by using a decomposition based multiobjective memetic algorithm. Memetic Comp. 15, 89–102 (2023). https://doi.org/10.1007/s12293-022-00370-z

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