Abstract
The ability to detect change-points in a dynamic network or a time series of graphs is an increasingly important task in many applications of the emerging discipline of graph signal processing. This paper formulates change-point detection as a hypothesis testing problem in terms of a generative latent position model, focusing on the special case of the Stochastic Block Model time series. We analyze two classes of scan statistics, based on distinct underlying locality statistics presented in the literature. Our main contribution is the derivation of the limiting properties and power characteristics of the competing scan statistics. Performance is compared theoretically, on synthetic data, and empirically, on the Enron email corpus.
Highlights
The change-point detection problem in a dynamic network is becoming increasingly prevalent in many applications of the emerging discipline of graph signal processing
An anomalous signal is broadly interpreted as constituting a deviation from some normal network pattern, e.g. a model-based characterization such as large scan statistics (c.f. § IV) or non-model based notions such as a community structure change, while a change-point is the time-window during which the anomaly appears
Priebe is with the Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD 21218 USA. but evolutionary anomalies that are maintained over a spatial or time window, i.e., the anomalous signal does not appears and disappears instantaneously In [3], the subgraph anomaly detection problem in static graphs were analyzed through likelihood ratio tests under a Poisson random graph model
Summary
The change-point detection problem in a dynamic network is becoming increasingly prevalent in many applications of the emerging discipline of graph signal processing. Using the locality statistic Ψ, [11] constructs fusion statistics of graphs for anomaly detection while [12] presents an analysis of the Enron data set to illustrate statistical inference for attributed random graphs All these cited works are mostly empirical in nature and do not provide much theoretical analysis of these locality-based scan statistics. Under the assumption that the time series of graphs is stationary before a change-point, we demonstrate in this paper that for τ = 1 and = 0, the limiting Sτ, ,k(t; Ψ) and Sτ, ,k(t; Φ) are the maximum of random variables which, under proper normalizations, follow a standard Gumbel G(0, 1) distribution in the limit Through these limiting properties, comparative power analysis between Sτ, ,k(t; Ψ) and Sτ, ,k(t; Φ) for τ = 1 and = 0 is performed We demonstrate that both Ψ and Φ are admissible if k = 0, while Ψ is inadmissible if k = 1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
