Monitoring attributed social networks based on count data and random effects

Document Type : Article

Authors

1 Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran

2 Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran

3 Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

Abstract

This paper presents a novel approach for the statistical monitoring of online social networks where the edges represent the count of communications between ties at each time stamp. Since the available methods in the literature are limited to the assumption that the set of all interacting individuals is fixed during the monitoring horizon and their corresponding attributes do not change over time, the proposed method tackles these limitations due to the properties of the random effects concepts. Applying appropriate parameters estimation technique involved in a likelihood ratio testing (LRT) approach considering two different statistics, the longitudinal network data are monitored. The performance of the proposed method is verified using numerical examples including simulation studies as well as an illustrative example.

Keywords


References:
[1] Erdös, P. and Rényi, A., “On random graphs”, I. PUBL MATH-DEBRECEN (Debrecen),6, pp. 290-297, (1959).
 [2] Leskovec, J., McGlohon, M., Faloutsos, C., Glance, N. and Hurst, M., “Patterns of cascading behaviour in large blog graphs”, Proceedings of the 2007 SIAM International conerence. on data mining, Society for Industriies and Applied Mathematics, USA, July, (2007).
[3] Tufekci, Z. and Wilson, C., “Social media and the decision to participate in political protest: Observations from Tahrir Square”, J. Commun, 62(2), pp. 363-379, (2012).
[4] Shetty, J. and Adibi, J., August. “Discovering important nodes through graph entropy the case of Enron email database”, In Proceedings of the 3rd International workshop on Link discovery, pp. 74-81, ACM, (2005).
[5] Krebs, V.E, “Mapping networks of terrorist cells”, Connections, 24(3), pp. 43-52, (2002).
[6] Pandit, V., Modani, N., Mukherjea, S., Nanavati, A.A., Roy, S. and Agarwal, A., January, “Extracting dense communities from telecom call graphs”, In Communication Systems Software and Middleware and Workshops, 2008. COMSWARE 2008. 3rd International Conference, pp. 82-89. IEEE, (2008).
[7] Savage, D., Zhang, X., Yu, X., Chou, P. and Wang, Q., “Anomaly detection in online social networks”, Soc. Netw, 39, PP. 62-70, (2014).
[8] Cheng, A. and Dickinson, P., “Using scan-statistical correlations for network change analysis”, Pacific-Asia Conference on Knowledge Discovery and Data Mining, Springer, Berlin, Heidelberg, (2013).
[9] McCulloh, I. and Carley, K.M., “Detecting change in longitudinal social networks Military Academy”, West Point NY Network Science Center (NSC), (2011).
[10] Miller, B.A., Arcelano, N., and , N.T. “Efficient anomaly detection in dynamic, attributed graphs: Emerging phenomena and big data”, IEEE International Conference on Intelligence and Security Informatics (ISI), USA, June, (2013).
[11] Bliss, C.A., Frank, M.R., Danforth, C.M. and Dodds, P.S, “An evolutionary algorithm approach to link prediction in dynamic social networks”, J Comput Sci-Neth, 5(5), pp.750-764, (2014).
[12] Woodall, W.H., Zhao, M.J., Paynabar, K., Sparks, R. and Wilson, J.D., “An overview and perspective on social network monitoring”, IEEE Trans. Ind. Appl.49(3): pp. 354-365, (2017).
[13] Heard, N.A., Weston, D.J., Platanioti, K., and Hand, D. J, “Bayesian anomaly detection methods for social networks”, Ann. Appl. Stat. 4(2), (2010).
[14] Priebe, C.E., Conroy, J.M., Marchette, D.J. and Park, Y, “Scan statistics on Enron graphs”, Comput. Math. Organ. Th., 11(3), pp. 229-247, (2005).
[15] Sparks, R., “Monitoring communications: aiming to identify periods of unusually increased communications between parties of interest”, Qual. Technol. Quant. M., 13(1): pp. 39-57, (2016).
[16] Neil, J., Hash, C., Brugh, A., Fisk, M., and Storlie, C.B., “Scan statistics for the online detection of locally anomalous subgraphs”, Technometrics, 55(4), pp. 403-414, (2013).
[17] Marchette, D., “Scan statistics on graphs”, Wiley Interdisciplinary Reviews, Computation Stat, 4(5), pp. 466-473, (2012).
[18] Pincombe, B., “Anomaly detection in time series of graphs using arma processes”, Australian Society for Operations Research Bulletin, 24(4), pp. 2-7, (2005).
[19] McCulloh, I. and Carley, K., “Detecting change in human social behaviour simulation”, Center for Computational Analysis of Social and Organizational Systems, Carnegie Mellon University, Pittsburgh, PA 15213, (2008a).
[20] McCulloh, I. and Carley, K., “Social network change detection”, Institute for Software Research School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213, (2008b).
[21] Azarnoush, B., Paynabar, K., Bekki, J., and Runger, G., “Monitoring temporal homogeneity in attributed network streams”, J Qual Technol, 48(1): pp. 28-43, (2016).
[22] Farahani, E.M., Baradaran Kazemzadeh, R., Noorossana, R. and Rahimian, G., “A statistical approach to social network monitoring”, Commun Stat-Theor M, 46(22): pp. 11272-11288, (2017).
[23] Fotuhi H, Amiri A, Maleki MR. “Phase I monitoring of social networks based on Poisson regression profiles”, Qual Reliab Eng Int, 34(4): pp. 1–17, (2018).
[24] Reisi-Gahrooei, M., Peynabar, K., “Change Detection in a Dynamic Stream of Attributed Networks”, arXiv preprint arXiv:1711.04441 (2018).
 [25] Woodall WH, Zhao MJ, Paynabar K, Sparks R, Wilson JD. “An overview and perspective on social network monitoring”, IEEE Trans. Ind. Appl. 2017; 49(3):354‐365.
[26] Sengupta, S, Woodall, WH. “Discussion of Statistical methods for network surveillance”, Appl Stoch Model Bus, 34(4): pp. 446-448, (2018).
[27] Hazrati‐Marangaloo, H, Noorossana, R. “Detecting outbreaks in temporally dependent networks”, Qual Reliab Eng Int, 35(6): pp. 1753-1765, (2019).
[28] Hosseini SS, Noorossana R. “Performance evaluation of EWMA and CUSUM control charts to detect anomalies in social networks using average and standard deviation of degree measures”, Qual Reliab Eng Int, 34(4): pp. 477-500, (2018).
[29] Yu, L., Woodall, W. H., & Tsui, K. L. “Detecting node propensity changes in the dynamic degree corrected stochastic block model”, Social Networks, 54: pp. 209-227, (2018).
[30] Sparks, R., “Detecting periods of significant increased communication levels for subgroups of targeted individuals”, Qual Reliab Eng Int, 32(5): pp. 1871-1888, (2016).
[31] Komolafe, T., Quevedo, A. V., Sengupta, S., & Woodall, W. H., “Statistical evaluation of spectral methods for anomaly detection in networks”, arXiv preprint arXiv:1711.01378, (2017).
[32] Mazrae Farahani E, Baradaran Kazemzade R, Albadvi A, Teimourpour B. “Modeling and monitoring social Network in term of longitudinal data”, Int. J. Ind. Eng. Comput., 29 (3): pp. 247-259, (2018).
[33] Hatef Fotuhi, Amirhossein Amiri & Ali Reza Taheriyoun  A novel approach based on multiple correspondence analysis for monitoring social networks with categorical attributed data, J Stat Comput Sim, 89(16), 3137-3164, (2019).
[34] Mogouie, H.,  Raissi-Ardali, G. A.,  Bahrami-Samani, E., Amiri  A., Statistical monitoring of binary response attributed social networks considering random effects, Published online in Commun Stat-Sim C, (2019). doi: 10.1080/03610918.2019.1661471.
[35] Najafi, H., Saghaei, A., Statistical monitoring for change detection of interactions between nodes in networks: with a case study in financial interactions network, Published online in Commun Stat-Theor M, (2020). doi: 10.1080/03610926.2020.1725830.
[36] Noorossana R, Hosseini SS, Heydarzade A. “An overview of dynamic anomaly detection in social networks via control charts”, Qual Reliab Eng Int, 34(4): pp. 641-648, (2018). 
[37] Myers, R.H., Montgomery, D.C., Vining, G.G., and Robinson, T.J., “Generalized linear models: with applications in engineering and the sciences”, John Wiley & Sons, (2012).
[38] Agresti, A., “Categorical data analysis”, John Wiley & Sons, (2013).
[39] Cameron, A.C. and Trivedi, P.K., “Regression analysis of count data”, (Vol. 53). Cambridge university press, (2013).