Bayesian Analysis

Latent Space Approaches to Community Detection in Dynamic Networks

Daniel K. Sewell and Yuguo Chen

Full-text: Open access

Abstract

Embedding dyadic data into a latent space has long been a popular approach to modeling networks of all kinds. While clustering has been done using this approach for static networks, this paper gives two methods of community detection within dynamic network data, building upon the distance and projection models previously proposed in the literature. Our proposed approaches capture the time-varying aspect of the data, can model directed or undirected edges, inherently incorporate transitivity and account for each actor’s individual propensity to form edges. We provide Bayesian estimation algorithms, and apply these methods to a ranked dynamic friendship network and world export/import data.

Article information

Source
Bayesian Anal., Volume 12, Number 2 (2017), 351-377.

Dates
First available in Project Euclid: 25 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ba/1461603847

Digital Object Identifier
doi:10.1214/16-BA1000

Mathematical Reviews number (MathSciNet)
MR3620737

Zentralblatt MATH identifier
1384.62203

Keywords
clustering longitudinal data Markov chain Monte Carlo mixture model Pólya–Gamma distribution variational Bayes

Rights
Creative Commons Attribution 4.0 International License.

Citation

Sewell, Daniel K.; Chen, Yuguo. Latent Space Approaches to Community Detection in Dynamic Networks. Bayesian Anal. 12 (2017), no. 2, 351--377. doi:10.1214/16-BA1000. https://projecteuclid.org/euclid.ba/1461603847


Export citation

References

  • Airoldi, E., Blei, D., Xing, E., and Fienberg, S. (2005). “A latent mixed membership model for relational data.” In Proceedings of the 3rd International Workshop on Link Discovery, 82–89. ACM.
  • Banerjee, A., Dhillon, I. S., Ghosh, J., and Sra, S. (2005). “Clustering on the unit hypersphere using von Mises-Fisher distributions.” Journal of Machine Learning Research, 6: 1345–1382.
  • Blasier, C. (1988). The Giant’s Rival: The USSR and Latin America. University of Pittsburgh Press.
  • Choi, H. M. and Hobert, J. P. (2013). “The Pólya–Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic.” Electronic Journal of Statistics, 7: 2054–2064.
  • Clauset, A., Newman, M. E., and Moore, C. (2004). “Finding community structure in very large networks.” Physical Review E, 70(6): 066111.
  • Cox, T. F. and Cox, M. A. (1991). “Multidimensional scaling on a sphere.” Communications in Statistics-Theory and Methods, 20(9): 2943–2953.
  • Csardi, G. and Nepusz, T. (2006). “The igraph software package for complex network research.” InterJournal, Complex Systems: 1695. http://igraph.org
  • Durante, D. and Dunson, D. B. (2014). “Nonparametric Bayes dynamic modelling of relational data.” Biometrika, 101(4): 883–898.
  • Fraley, C. and Raftery, A. E. (2007). “Bayesian regularization for normal mixture estimation and model-based clustering.” Journal of Classification, 24(2): 155–181.
  • Gormley, I. C. and Murphy, T. B. (2010). “A mixture of experts latent position cluster model for social network data.” Statistical Methodology, 7(3): 385–405.
  • Grier, R. M. (1999). “Colonial legacies and economic growth.” Public Choice, 98(3–4): 317–335.
  • Handcock, M. S., Raftery, A. E., and Tantrum, J. M. (2007). “Model-based clustering for social networks.” Journal of the Royal Statistical Society: Series A, 170(2): 301–354.
  • Hanneke, S., Fu, W., and Xing, E. P. (2010). “Discrete temporal models of social networks.” Electronic Journal of Statistics, 4: 585–605.
  • Hoff, P. D., Raftery, A. E., and Handcock, M. S. (2002). “Latent space approaches to social network analysis.” Journal of the American Statistical Association, 97(460): 1090–1098.
  • Holland, P. W., Laskey, K. B., and Leinhardt, S. (1983). “Stochastic blockmodels: first steps.” Social Networks, 5(2): 109–137.
  • Krivitsky, P. N. and Butts, C. T. (2012). “Exponential-family random graph models for rank-order relational data.” arXiv:1210.0493.
  • Krivitsky, P. N. and Handcock, M. S. (2008). “Fitting position latent cluster models for social networks with latentnet.” Journal of Statistical Software, 24(5): 1–23.
  • Krivitsky, P. N. and Handcock, M. S. (2015). latentnet: Latent Position and Cluster Models for Statistical Networks. The Statnet Project (http://www.statnet.org). R package version 2.7.1. http://CRAN.R-project.org/package=latentnet.
  • Krivitsky, P. N., Handcock, M. S., Raftery, A. E., and Hoff, P. D. (2009). “Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models.” Social Networks, 31(3): 204–213.
  • Leifeld, P., Cranmer, S. J., and Desmarais, B. A. (2015). xergm: Extensions for Exponential Random Graph Models. R package version 1.5.9. http://CRAN.R-project.org/package=xergm.
  • Meilă, M. (2003). “Comparing clusterings by the variation of information.” In Learning Theory and Kernel Machines, 173–187. Springer.
  • Moody, J., McFarland, D., and Bender-deMoll, S. (2005). “Dynamic network visualization.” American Journal of Sociology, 110(4): 1206–1241.
  • Nakao, K. and Romney, A. K. (1993). “Longitudinal approach to subgroup formation: Re-analysis of Newcomb’s fraternity data.” Social Networks, 15(2): 109–131.
  • Newcomb, T. M. (1956). “The prediction of interpersonal attraction.” American Psychologist, 11(11): 575–586.
  • Papastamoulis, P. and Iliopoulos, G. (2010). “An artificial allocations based solution to the label switching problem in Bayesian analysis of mixtures of distributions.” Journal of Computational and Graphical Statistics, 19(2): 313–331.
  • Plackett, R. (1975). “The analysis of permutations.” Applied Statistics, 24(2): 193–202.
  • Plummer, M., Best, N., Cowles, K., and Vines, K. (2006). “CODA: Convergence diagnosis and output analysis for MCMC.” R News, 6(1): 7–11. http://CRAN.R-project.org/doc/Rnews/.
  • Polson, N. G., Scott, J. G., and Windle, J. (2013). “Bayesian inference for logistic models using Pólya–Gamma latent variables.” Journal of the American Statistical Association, 108(504): 1339–1349.
  • Raftery, A. E., Niu, X., Hoff, P. D., and Yeung, K. Y. (2012). “Fast inference for the latent space network model using a case-control approximate likelihood.” Journal of Computational and Graphical Statistics, 21(4): 901–919.
  • Salter-Townshend, M. and Murphy, T. B. (2013). “Variational Bayesian inference for the latent position cluster model for network data.” Computational Statistics & Data Analysis, 57(1): 661–671.
  • Sarkar, P. and Moore, A. (2005). “Dynamic social network analysis using latent space models.” ACM SIGKDD Explorations Newsletter, 7(2): 31–40.
  • Scott, J. G. and Sun, L. (2013). “Expectation-maximization for logistic regression.” arXiv:1306.0040.
  • Sewell, D. K. and Chen, Y. (2015a). “Analysis of the formation of the structure of social networks using latent space models for ranked dynamic networks.” Journal of the Royal Statistical Society: Series C, 64: 611–633.
  • Sewell, D. K. and Chen, Y. (2015b). “Latent space models for dynamic networks.” Journal of the American Statistical Association, 110(512): 1646–1657.
  • Sewell, D. K. and Chen, Y. (2016a). “Latent space models for dynamic networks with weighted edges.” Social Networks, 44: 105–116.
  • Sewell, D. K. and Chen, Y. (2016b). “Supplementary Material for “Latent Space Approaches to Community Detection in Dynamic Networks”.” Bayesian Analysis.
  • Sewell, D. K., Chen, Y., Bernhard, W., and Sulkin, T. (2016). “Model-based longitudinal clustering with varying cluster assignments.” Statistica Sinica, 26(1): 205–233.
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and Van Der Linde, A. (2002). “Bayesian measures of model complexity and fit.” Journal of the Royal Statistical Society: Series B, 64(4): 583–639.
  • Xing, E. P., Fu, W., and Song, L. (2010). “A state-space mixed membership blockmodel for dynamic network tomography.” The Annals of Applied Statistics, 4(2): 535–566.

Supplemental materials