TY - JOUR

T1 - A robust information source estimator with sparse observations

AU - Zhu, Kai

AU - Ying, Lei

N1 - Funding Information:
This research was supported in part by ARO grant W911NF-13-1-0279.
Publisher Copyright:
© 2014, Zhu and Ying; licensee Springer.

PY - 2014/12/1

Y1 - 2014/12/1

N2 - Purpose/Background: In this paper, we consider the problem of locating the information source with sparse observations. We assume that a piece of information spreads in a network following a heterogeneous susceptible-infected-recovered (SIR) model, where a node is said to be infected when it receives the information and recovered when it removes or hides the information. We further assume that a small subset of infected nodes are reported, from which we need to find the source of the information. Methods: We adopt the sample path-based estimator developed in the work of Zhu and Ying (arXiv:1206.5421, 2012) and prove that on infinite trees, the sample path-based estimator is a Jordan infection center with respect to the set of observed infected nodes. In other words, the sample path-based estimator minimizes the maximum distance to observed infected nodes. We further prove that the distance between the estimator and the actual source is upper bounded by a constant independent of the number of infected nodes with a high probability on infinite trees. Results: Our simulations on tree networks and real-world networks show that the sample path-based estimator is closer to the actual source than several other algorithms. Conclusions: In this paper, we proposed the sample path-based estimator for information source localization. Both theoretic analysis and numerical evaluations showed that the sample path-based estimator is robust and close to the real source.

AB - Purpose/Background: In this paper, we consider the problem of locating the information source with sparse observations. We assume that a piece of information spreads in a network following a heterogeneous susceptible-infected-recovered (SIR) model, where a node is said to be infected when it receives the information and recovered when it removes or hides the information. We further assume that a small subset of infected nodes are reported, from which we need to find the source of the information. Methods: We adopt the sample path-based estimator developed in the work of Zhu and Ying (arXiv:1206.5421, 2012) and prove that on infinite trees, the sample path-based estimator is a Jordan infection center with respect to the set of observed infected nodes. In other words, the sample path-based estimator minimizes the maximum distance to observed infected nodes. We further prove that the distance between the estimator and the actual source is upper bounded by a constant independent of the number of infected nodes with a high probability on infinite trees. Results: Our simulations on tree networks and real-world networks show that the sample path-based estimator is closer to the actual source than several other algorithms. Conclusions: In this paper, we proposed the sample path-based estimator for information source localization. Both theoretic analysis and numerical evaluations showed that the sample path-based estimator is robust and close to the real source.

KW - Heterogeneous SIR model

KW - Information source detection

KW - Sparse observation

UR - http://www.scopus.com/inward/record.url?scp=84946067589&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946067589&partnerID=8YFLogxK

U2 - 10.1186/s40649-014-0003-2

DO - 10.1186/s40649-014-0003-2

M3 - Article

AN - SCOPUS:84946067589

VL - 1

JO - Computational Social Networks

JF - Computational Social Networks

SN - 2197-4314

IS - 1

M1 - 3

ER -