Estimating Infection Sources in Networks Using Partial Timestamps

Abstract

We study the problem of identifying infection sources in a network based on the network topology, and a subset of infection timestamps. In the case of a single infection source in a tree network, we derive the maximum likelihood estimator of the source and the unknown diffusion parameters. We then introduce a new heuristic involving an optimization over a parametrized family of Gromov matrices to develop a single source estimation algorithm for general graphs. Compared with the breadth-first search tree heuristic commonly adopted in the literature, simulations demonstrate that our approach achieves better estimation accuracy than several other benchmark algorithms, even though these require more information like the diffusion parameters. We next develop a multiple sources estimation algorithm for general graphs, which first partitions the graph into source candidate clusters, and then applies our single source estimation algorithm to each cluster. We show that if the graph is a tree, then each source candidate cluster contains at least one source. Simulations using synthetic and real networks, and experiments using real-world data suggest that our proposed algorithms are able to estimate the true infection source(s) to within a small number of hops with a small portion of the infection timestamps being observed.

Locating the Source of Diffusion in Complex Networks via Gaussian-Based Localization and Deduction

“…Although we only present the optimization process for undirected networks, the corresponding formula for directed networks can be easily achieved via slight modifications. Upon we finish our work, we notice a recent paper proposed by Tang et al [35] that also combines parameter estimation with source localization. Their approach is more complicated than ours since they treat more diffusion parameters as unknown and perform the optimization over a parameterized family of Gromov matrices.…”

On the Properties of Gromov Matrices and Their Applications in Network Inference

“…Suppose for a base (T, s, V ), T spans V ∪ {s}. Proposition 1 of [21] may be generalized (using a similar proof) as follows: for each Gromov matrix, its base is uniquely determined, up to isometric equivalence. This observation tells us that the Gromov matrix contains all the information we want to describe a base.…”

“…Here, we assume that a small percentage of the infected nodes are observed, together with their respective infection timestamps. We apply the Gromov method (using convex combination), similar to the snapshot observation based estimation described above (we refer the reader to [21] for details). We compare the Gromov method with the BFS tree based approach (called BFS-MLE), as well as other approaches: GAU [10] and TRBS [33], on various networks.…”

Locating multiple information sources in social networks based on the naming game

“…Fu et al [12] propose a backward diffusion-based source localization method and find that multiple sources can be located with high accuracy even when the fraction of observers is small and the time delay along the links is not known exactly. Tang et al [13] introduce a new heuristic involving an optimization over a parametrized family of Gromov matrices to develop an estimation algorithm for both a single source and multiple sources. However, the above studies assume that the propagation delays along each edge and the number of sources are known.…”