## Annals of Applied Statistics

### Identifying overlapping terrorist cells from the Noordin Top actor–event network

#### Abstract

Actor–event data are common in sociological settings, whereby one registers the pattern of attendance of a group of social actors to a number of events. We focus on 79 members of the Noordin Top terrorist network, who were monitored attending 45 events. The attendance or nonattendance of the terrorist to events defines the social fabric, such as group coherence and social communities. The aim of the analysis of such data is to learn about the affiliation structure. Actor–event data is often transformed to actor–actor data in order to be further analysed by network models, such as stochastic block models. This transformation and such analyses lead to a natural loss of information, particularly when one is interested in identifying, possibly overlapping, subgroups or communities of actors on the basis of their attendances to events. In this paper we propose an actor–event model for overlapping communities of terrorists which simplifies interpretation of the network. We propose a mixture model with overlapping clusters for the analysis of the binary actor–event network data, called $\mathtt{manet}$, and develop a Bayesian procedure for inference. After a simulation study, we show how this analysis of the terrorist network has clear interpretative advantages over the more traditional approaches of affiliation network analysis.

#### Article information

Source
Ann. Appl. Stat., Volume 14, Number 3 (2020), 1516-1534.

Dates
Revised: August 2019
First available in Project Euclid: 18 September 2020

https://projecteuclid.org/euclid.aoas/1600454877

Digital Object Identifier
doi:10.1214/20-AOAS1358

Mathematical Reviews number (MathSciNet)
MR4152144

#### Citation

Ranciati, Saverio; Vinciotti, Veronica; Wit, Ernst C. Identifying overlapping terrorist cells from the Noordin Top actor–event network. Ann. Appl. Stat. 14 (2020), no. 3, 1516--1534. doi:10.1214/20-AOAS1358. https://projecteuclid.org/euclid.aoas/1600454877

#### References

• Airoldi, E. M., Blei, D. M., Fienberg, S. E. and Xing, E. P. (2008). Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9 1981–2014.
• Aitkin, M., Vu, D. and Francis, B. (2017). Statistical modelling of a terrorist network. J. Roy. Statist. Soc. Ser. A 180 751–768.
• Celeux, G., Forbes, F., Robert, C. P. and Titterington, D. M. (2006). Deviance information criteria for missing data models. Bayesian Anal. 1 651–673.
• Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging. Cambridge Series in Statistical and Probabilistic Mathematics 27. Cambridge Univ. Press, Cambridge.
• Daudin, J.-J., Picard, F. and Robin, S. (2008). A mixture model for random graphs. Stat. Comput. 18 173–183.
• Doreian, P., Batagelj, V. and Ferligoj, A. (2004). Generalized blockmodeling of two-mode network data. Soc. Netw. 26 29–53.
• Durante, D. and Dunson, D. B. (2014). Nonparametric Bayes dynamic modelling of relational data. Biometrika 101 883–898.
• Everton, S. F. (2012). Disrupting Dark Networks. Structural Analysis in the Social Sciences 34. Cambridge Univ. Press, Cambridge.
• Frank, O. and Strauss, D. (1986). Markov graphs. J. Amer. Statist. Assoc. 81 832–842.
• Goldenberg, A., Zheng, A. X., Fienberg, S. E., Airoldi, E. M. et al. (2010). A survey of statistical network models. Found. Trends Mach. Learn. 2 129–233.
• Handcock, M. S., Raftery, A. E. and Tantrum, J. M. (2007). Model-based clustering for social networks. J. Roy. Statist. Soc. Ser. A 170 301–354.
• Hoff, P. D., Raftery, A. E. and Handcock, M. S. (2002). Latent space approaches to social network analysis. J. Amer. Statist. Assoc. 97 1090–1098.
• Holland, P. W., Laskey, K. B. and Leinhardt, S. (1983). Stochastic blockmodels: First steps. Soc. Netw. 5 109–137.
• International Crisis Group (2009). Indonesia: Noordin Top’s support base. Asia Briefing 95. Available at http://www.refworld.org/docid/4a968a982.html.
• Kolaczyk, E. D. (2009). Statistical Analysis of Network Data: Methods and Models. Springer Series in Statistics. Springer, New York.
• Leger, J. B. (2015). Blockmodels: Latent and stochastic block model estimation by a V-EM algorithm. R package version 1.
• Neal, Z. (2014). The backbone of bipartite projections: Inferring relationships from co-authorship, co-sponsorship, co-attendance and other co-behaviors. Soc. Netw. 39 84–97.
• Nowicki, K. and Snijders, T. A. B. (2001). Estimation and prediction for stochastic blockstructures. J. Amer. Statist. Assoc. 96 1077–1087.
• Plummer, M., Best, N., Cowles, K. and Vines, K. (2006). CODA: Convergence diagnosis and output analysis for MCMC. R News 6 7–11.
• 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. J. Comput. Graph. Statist. 21 901–919.
• Ranciati, S., Vinciotti, V. and Wit, E. C. (2020). Supplement to “Identifying overlapping terrorist cells from the Noordin Top actor–event network.” https://doi.org/10.1214/20-AOAS1358SUPP
• Ranciati, S., Viroli, C. and Wit, E. C. (2017). Mixture model with multiple allocations for clustering spatially correlated observations in the analysis of ChIP-Seq data. Biom. J. 59 1301–1316.
• Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. J. Amer. Statist. Assoc. 66 846–850.
• Robins, G., Snijders, T., Wang, P., Handcock, M. and Pattison, P. (2007). Recent developments in exponential random graph (p*) models for social networks. Soc. Netw. 29 192–215.
• Sewell, D. K. and Chen, Y. (2017). Latent space approaches to community detection in dynamic networks. Bayesian Anal. 12 351–377.
• Signorelli, M. and Wit, E. C. (2018). A penalized inference approach to stochastic block modelling of community structure in the Italian Parliament. J. R. Stat. Soc. Ser. C. Appl. Stat. 67 355–369.
• Skvoretz, J. and Faust, K. (1999). Logit models for affiliation networks. Sociol. Method. 29 253–280.
• Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B. Stat. Methodol. 64 583–639.
• Stephens, M. (2000). Dealing with label switching in mixture models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 62 795–809.
• Wang, Y. J. and Wong, G. Y. (1987). Stochastic blockmodels for directed graphs. J. Amer. Statist. Assoc. 82 8–19.
• Wang, P., Sharpe, K., Robins, G. L. and Pattison, P. E. (2009). Exponential random graph (p*) models for affiliation networks. Soc. Netw. 31 12–25.
• Wasserman, S. and Faust, K. (1994). Social Network Analysis: Methods and Applications. Structural Analysis in the Social Sciences 8. Cambridge Univ. Press, Cambridge.
• Wasserman, S. and Pattison, P. (1996). Logit models and logistic regressions for social networks. I. An introduction to Markov graphs and $p$. Psychometrika 61 401–425.
• Xing, E. P., Fu, W. and Song, L. (2010). A state-space mixed membership blockmodel for dynamic network tomography. Ann. Appl. Stat. 4 535–566.

#### Supplemental materials

• Supplement to “Identifying overlapping terrorist cells from the Noordin Top actor–event network”. The supplementary material contains two additional toy examples, the sketch of the algorithm, and further results on the application discussed in the main manuscript.