Harmonic space-time threat propagation for graph detection

Abstract

This paper addresses threat propagation on space-time graphs, defined to be a time-sampled graph. The application considered is geographical sites connected by tracks, though such graphs arise in many fields. Several new concepts and efficient algorithms are introduced, specifically, the space-time adjacency matrix and harmonic threat propagation. The cued threat propagation problem is shown to be equivalent to the harmonic solution to Laplace's equation on the graph. Alternately, the Perron-Frobenius theorem is applied to a modified space-time adjacency matrix to derive a concept of eigen-threat on space-time graphs. Both approaches yield fast, scalable algorithms for space-time threat propagation applicable to both very small and very large graphs. Algorithms are motivated by a continuous time stochastic process model. Detection performance is shown using a simulated insurgent network data for which harmonic space-time threat propagation achieves an 84% probability of detection with a 4% false alarm probability over the entire graph.

A Spectral Framework for Anomalous Subgraph Detection

“…The smallest (i.e., most negative) value is then used as a test statistic, since we are interested in cases where the norm is small. The test statistic is given by (16) An example demonstrating this method is provided in Fig. 3.…”

“…Other work assumes common substructures over the graph, and detects anomalies based on deviations from the "normative pattern" via methods such as minimum description length [14] or analysis of the graph Laplacian [15]. Techniques such as threat propagation [16], [17] and vertex nomination [18] consider a cue vertex as a knowledge prior, giving an initial indication of which vertices are of interest, the objective then being to find the remainder of the subgraph. Community detection in graphs is a widely studied related problem [19], where the communities in the graph are sometimes cast as deviations from a null hypothesis in which the graph has no community structure [20].…”

Probabilistic threat propagation for malicious activity detection

“…In future work, we will analyze different edge weighting functions [11] and see how our method fits with noniterative solutions [13]. Finally, we will apply PTP towards non-malicious communities, propagating 'trust' as an example, or even multiple communities of interest.…”

“…Recent methods [11,12,13] take an iterative approach in which 'threat' is initialized at the tip nodes and iteratively propagated throughout the graph. These methods have proven promising, yet suffer from what we deem as direct feedback, in which a node's threat level can increase solely based on the threat it had previously propagated to neighbors.…”

Bayesian Discovery of Threat Networks

“…Space-Time threat propagation is used compute the time-varying threat across a graph given one or more observations at specific vertices and times [48], [57]. In such scenarios, the time-stamped graph may be viewed as a space-time graph where is the set of sample times and is an edge set determined by the temporal correlations between vertices at specific times.…”