Multi-objective Optimization with Nonnegative Matrix Factorization for Identifying Overlapping Communities in Networks

  • Hongmin Liu
  • Hao LiEmail author
  • Wei Zhao
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 682)


Community structure is one of the most important properties existing in complex networks, and community detection in complex networks is an intensively investigated problem in recent years. In real-world networks, a node is usually shared by several overlapping communities. The problem of detecting overlapping communities is much more complicated than the hard-partition problem. In this paper, a multi-objective immune algorithm with nonnegative matrix factorization as local search module (MOIA-Net) is proposed to uncover overlapping communities in networks. The proposed algorithm simultaneously optimizes two criteria, negative ratio association and ratio cut, to achieve a preferable soft-partition in networks. It adopts a nonnegative matrix factorization strategy as local search procedure to enhance the search ability. Experiments on synthetic networks show the efficiency of the proposed algorithm.


Complex network Overlapping community detection Multi-objective optimization Nonnegative matrix factorization 


  1. 1.
    Angelini, L., Boccaletti, S., Marinazzo, D., Pellicoro, M., Stramaglia, S.: Identification of network modules by optimization of ratio association. Chaos 17(2), 023114 (2007)CrossRefzbMATHGoogle Scholar
  2. 2.
    Clauset, A., Newman, M.E., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70(6), 066111 (2004)CrossRefGoogle Scholar
  3. 3.
    Danon, L., Diaz-Guilera, A., Duch, J., Arenas, A.: Comparing community structure identification. J. Stat. Mech. 2005(09), P09008 (2005)CrossRefGoogle Scholar
  4. 4.
    Gong, M., Jiao, L., Du, H., Bo, L.: Multiobjective immune algorithm with nondominated neighbor-based selection. Evol. Comput. 16(2), 225–255 (2008)CrossRefGoogle Scholar
  5. 5.
    Gong, M., Ma, L., Zhang, Q., Jiao, L.: Community detection in networks by using multiobjective evolutionary algorithm with decomposition. Phys. A 391(15), 4050–4060 (2012)CrossRefGoogle Scholar
  6. 6.
    Lancichinetti, A., Fortunato, S.: Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys. Rev. E. 80(1), 016118 (2009)CrossRefGoogle Scholar
  7. 7.
    Lancichinetti, A., Fortunato, S., Kertész, J.: Detecting the overlapping and hierarchical community structure in complex networks. New J. Phys. 11(3), 033015 (2009)CrossRefGoogle Scholar
  8. 8.
    Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 814–818 (2005)CrossRefGoogle Scholar
  9. 9.
    Pizzuti, C.: A multi-objective genetic algorithm for community detection in networks. In: Proceedings of IEEE International Conference on Tools with Artificial Intelligence, pp. 379–386 (2009)Google Scholar
  10. 10.
    Psorakis, I., Roberts, S., Ebden, M., Sheldon, B.: Overlapping community detection using bayesian non-negative matrix factorization. Phys. Rev. E 83(6), 066114 (2011)CrossRefGoogle Scholar
  11. 11.
    Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. Proc. Natl. Acad. Sci. USA 105(4), 1118–1123 (2008)CrossRefGoogle Scholar
  12. 12.
    Tan, V.Y., Févotte, C.: Automatic relevance determination in nonnegative matrix factorization. In: Proceedings of Signal Processing with Adaptive Sparse Structured Representations (2009)Google Scholar
  13. 13.
    Wei, Y.C., Cheng, C.K.: Ratio cut partitioning for hierarchical designs. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 10(7), 911–921 (1991)CrossRefGoogle Scholar
  14. 14.
    Zhang, P., Moore, C., Newman, M.: Community detection in networks with unequal groups. Phys. Rev. E 93(1), 012303 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  1. 1.School of Computer Science and TechniqueHenan Polytechnic UniversityJiaozuoChina
  2. 2.Key Laboratory of Intelligent Perception and Image UnderstandingXidian UniversityXi’anChina
  3. 3.School of Computer Science and TechnologyXidian UniversityXi’anChina

Personalised recommendations