Detecting outbreaks in temporally dependent networks

Abstract

Dynamic networks require effective methods of monitoring and surveillance in order to respond promptly to unusual disturbances. In many applications, it is of interest to identify anomalous behavior within a dynamic interacting system. Such anomalous interactions are reflected by structural changes in the network representation of the system. In this paper, a dynamic random graph model is proposed that takes into account the past activities of the individuals in the social network and also represents temporal dependency of the network. The model parameters are appearance and disappearance probabilities of an edge which are estimated using a maximum likelihood approach.A generalization of a single path-dependent likelihood ratio test is employed to detect changes in the parameters of the proposed model. Through monitoring the estimated parameters, one can effectively detect structural changes in a temporal-dependent network. The proposed model is employed to describe the behavior of a real network, and its parameters are monitored via dependent likelihood ratio test and multivariate exponentially weighted moving average control chart. Results indicate that the proposed dynamic random graph model is a reliable mean to modeling and detecting changes in temporally dependent networks.KEYWORDS degree-corrected stochastic block model, dynamic network, multivariate exponentially weighted moving average, temporally dependent network longitudinal network data set, the Noordin Top terrorist network from 2001 to 2010, to evaluate the applicability of recently developed methods for social network change detection (SNCD). Application of change detection methods to this historical data set illustrated their potential usefulness including its ability to detect significant changes in the network in response to a series of exogenous factors such as acquisition of bombing materials, capture of key leaders and groups, and death of Noordin himself. Such instances reveal the utmost importance of devising practical network surveillance plans which may help to study complex systems. There are several studies which use process control charts to monitor network behavior. Mcculloh and Carley 6-8 applied cumulative sum (CUSUM) chart to monitor changes in military networks. They employed network metrics, including centrality, betweenness, average link density, and average degree, as features to monitor the network. Since most of the network topological metrics do not follow a normal distribution 9 and also most of the CUSUM procedures are sensitive to the normality assumptions, one should be aware of how normality assumptions may affect the performance of the CUSUM control chart.Considering nine invariants to represent a graph snapshot including network metrics and scaled scan statistics, Park et al 10 proposed a statistic comprised of a weighted sum of the network invariants, and an anomaly was detected when the weighted sum statistic was significantly large. Park et al 11 employed a hypergraph to model a social network and proposed a scan ...

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