Advertisement

Neural Computing and Applications

, Volume 29, Issue 9, pp 413–424 | Cite as

Structural regularity exploration in multidimensional networks via Bayesian inference

  • Yi Chen
  • Xiaolong Wang
  • Buzhou Tang
ICONIP 2015
  • 101 Downloads

Abstract

Multidimensional networks, networks with multiple kinds of relations, widely exist in various fields in the real world, such as sociology, chemistry, biology and economics. One fundamental task of network analysis is to explore network structure, including assortative structure (i.e., community structure), disassortative structure (e.g., bipartite structure) and mixture structure, that is, to find structural regularities in networks. There are two aspects of structural regularity exploration: (1) group partition—how to partition nodes of networks into different groups, and (2) group number—how many groups in networks. Most existing structural regularity exploration methods for multidimensional networks need to pre-assume the structure type (e.g., the community structure) and to give the group number of networks, among which the structure type is a guide to group partition. However, the structure type and group number are usually unavailable in advance. To explore structural regularities in multidimensional networks well without pre-assuming which type of structure they have, we propose a novel feature aggregation method based on a mixture model and Bayesian theory, called the multidimensional Bayesian mixture (MBM) model. To automatically determine the group number of multidimensional networks, we further extend the MBM model using Bayesian nonparametric theory to a new model, called the multidimensional Bayesian nonparametric mixture (MBNPM) model. Experiments conducted on a number of synthetic and real multidimensional networks show that the MBM model outperforms other related models on most networks and the MBNPM model is comparable to the MBM model.

Keywords

Multidimensional networks Network structure Structural regularity exploration Mixture model Bayesian nonparametric theory 

Notes

Acknowledgements

This paper is supported in part by Grants: National 863 Program of China (2015AA015405), NSFCs (National Natural Science Foundations of China) (61573118, 61402128, 61473101 and 61472428), Special Foundation for Technology Research Program of Guangdong Province (2015B010131010), Strategic Emerging Industry Development Special Funds of Shenzhen (20151013161937, JSGG20151015161015297 and JCYJ20160531192358466), Innovation Fund of Harbin Institute of Technology (HIT.NSRIF.2017052), Program from the Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education (93K172016K12) and CCF-Tencent Open Research Fund (RAGR20160102).

Compliance with ethical standards

Conflict of interest

The article is an extension of the paper entitled “Structural regularity exploration in multidimensional networks” published in the 22nd International Conference on Neural Information Processing (ICONIP 2015).

Supplementary material

521_2017_3041_MOESM1_ESM.doc (268 kb)
Supplementary material 1 (DOC 268 kb)

References

  1. 1.
    de Franciscis S, Caravagna G, d’Onofrio A (2016) Gene switching rate determines response to extrinsic perturbations in a transcriptional network motif. Sci Rep 6:26980. doi: 10.1038/srep26980 CrossRefGoogle Scholar
  2. 2.
    Newman M, Clauset A (2015) Structure and inference in annotated networks. Nat Commun 7:11863. doi: 10.1038/ncomms11863 CrossRefGoogle Scholar
  3. 3.
    Coyte KZ, Schluter J, Foster KR (2015) The ecology of the microbiome: networks, competition, and stability. Science 350(6261):663–666. doi: 10.1126/science.aad2602 CrossRefGoogle Scholar
  4. 4.
    Neftci E et al (2013) Synthesizing cognition in neuromorphic electronic systems. Proc Natl Acad Sci 110(37):E3468–E3476. doi: 10.1073/pnas.1212083110 CrossRefGoogle Scholar
  5. 5.
    Newman ME, Leicht EA (2007) Mixture models and exploratory analysis in networks. Proc Natl Acad Sci 104(23):9564–9569. doi: 10.1073/pnas.0610537104 CrossRefzbMATHGoogle Scholar
  6. 6.
    Chai B-F et al (2013) Combining a popularity-productivity stochastic block model with a discriminative-content model for general structure detection. Phys Rev E 88(1):012807. doi: 10.1103/PhysRevE.88.012807 CrossRefGoogle Scholar
  7. 7.
    Zhu G, Li K (2014) A unified model for community detection of multiplex networks. In: International conference on web information systems engineering. Springer. doi: 10.1007/978-3-319-11749-2_3
  8. 8.
    Tang L, Liu H (2009) Uncovering cross-dimension group structures in multi-dimensional networks. In: SDM workshop on analysis of dynamic networks. Sparks, NVGoogle Scholar
  9. 9.
    Boden B et al (2013) RMiCS: a robust approach for mining coherent subgraphs in edge-labeled multi-layer graphs. In: Proceedings of the 25th international conference on scientific and statistical database management. ACM. doi: 10.1007/s10618-012-0272-z
  10. 10.
    Mucha PJ et al (2010) Community structure in time-dependent, multiscale, and multiplex networks. Science 328(5980):876–878. doi: 10.1126/science.1184819
  11. 11.
    DuBois C, Smyth P (2010) Modeling relational events via latent classes. In: Proceedings of the 16th ACM SIGKDD international conference on knowledge discovery and data mining. ACM. doi: 10.1145/1835804.1835906
  12. 12.
    Sinkkonen J et al (2008) A simple infinite topic mixture for rich graphs and relational data. In: Proceedings of the NIPS workshop on analyzing graphs: theory and applications. CiteseerGoogle Scholar
  13. 13.
    Xu Z, Kersting K, Tresp V (2009) Multi-relational learning with Gaussian processes. In: IJCAI. doi: 10.1145/1390334.1390380
  14. 14.
    Gershman SJ, Blei DM (2012) A tutorial on Bayesian nonparametric models. J Math Psychol 56(1):1–12. doi: 10.1016/j.jmp.2011.08.004
  15. 15.
    Battiston F, Nicosia V, Latora V (2014) Structural measures for multiplex networks. Phys Rev E 89(3):032804. doi: 10.1103/PhysRevE.89.032804
  16. 16.
    Tang L, Wang X, Liu H (2010) Community detection in multi-dimensional networks. Computer Science and Engineering, Arizona State University, TempeGoogle Scholar
  17. 17.
    Berlingerio M, Pinelli F, Calabrese F (2013) Abacus: frequent pattern mining-based community discovery in multidimensional networks. Data Min Knowl Disc 27(3):294–320. doi: 10.1007/s10618-013-0331-0
  18. 18.
    Wu Z et al (2013) Community detection in multi-relational social networks. In: International conference on web information systems engineering. Springer. doi: 10.1007/978-3-642-41154-0_4
  19. 19.
    Carchiolo V et al (2011) Communities unfolding in multislice networks. In: Complex networks. Springer, pp 187–195. doi: 10.1007/978-3-642-25501-4_19
  20. 20.
    Shen H-W, Cheng X-Q, Guo J-F (2011) Exploring the structural regularities in networks. Phys Rev E 84(5):056111. doi: 10.1103/PhysRevE.84.056111
  21. 21.
    Chen Y et al (2014) Overlapping community detection in networks with positive and negative links. J Stat Mech Theory Exp 2014(3):P03021. doi: 10.1088/1742-5468/2014/03/P03021
  22. 22.
    Khoshneshin M, Street N (2013) A graphical model for multi-relational social network analysis. Relation 4(K3):K4Google Scholar
  23. 23.
    Kemp C et al (2006) Learning systems of concepts with an infinite relational model. In: AAAI. doi: 10.1145/1102351.1102407
  24. 24.
    Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B (Methodological) 1–38Google Scholar
  25. 25.
    Palla K, Knowles DA, Ghahramani Z (2012) An infinite latent attribute model for network data. In: International conference on machine learningGoogle Scholar
  26. 26.
    Andrieu C et al (2003) An introduction to MCMC for machine learning. Mach Learn 50(1–2):5–43. doi: 10.1023/A:1020281327116
  27. 27.
    Neal RM (2003) Slice sampling. Ann Stat. doi: 10.1214/aos/1056562461 MathSciNetzbMATHGoogle Scholar
  28. 28.
    Rodriguez A, Laio A (2014) Clustering by fast search and find of density peaks. Science 344(6191):1492–1496. doi: 10.1126/science.1242072 CrossRefGoogle Scholar
  29. 29.
    Ana L, Jain AK (2003) Robust data clustering. In: Proceedings of 2003 IEEE computer society conference on computer vision and pattern recognition, 2003. IEEE. doi: 10.1109/CVPR.2003.1211462
  30. 30.
    Coleman J, Katz E, Menzel H (1957) The diffusion of an innovation among physicians. Sociometry 20(4):253–270. doi: 10.2307/2785979 CrossRefGoogle Scholar
  31. 31.
    Nooy W (2006) Interlock formation an actor-oriented approach. In: Politics and interlocking directorates conference. MIT PressGoogle Scholar
  32. 32.
    Snijders TA et al (2006) New specifications for exponential random graph models. Sociol Methodol 36(1):99–153. doi: 10.1111/j.1467-9531.2006.00176.x CrossRefGoogle Scholar
  33. 33.
    Handcock MS et al (2003) statnet: an R package for the statistical modeling of social networks. http://www.csde.washington.edu/statnet
  34. 34.
    Ulanowicz RE, DeAngelis DL (2005) Network analysis of trophic dynamics in South Florida ecosystems. US Geological Survey Program on the South Florida Ecosystem, vol 114Google Scholar
  35. 35.
    Jacob Y, Denoyer L, Gallinari P (2011) Classification and annotation in social corpora using multiple relations. In: Proceedings of the 20th ACM international conference on information and knowledge management. ACM. doi: 10.1016/j.ins.2009.01.007

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyShenzhen Graduate School, Harbin Institute of TechnologyShenzhenChina
  2. 2.School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina

Personalised recommendations