### Abstract

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.

Original language | English (US) |
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Article number | 3 |

Journal | Computational Social Networks |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2014 |

Externally published | Yes |

### Keywords

- Heterogeneous SIR model
- Information source detection
- Sparse observation

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Human-Computer Interaction
- Modeling and Simulation

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## Cite this

*Computational Social Networks*,

*1*(1), [3]. https://doi.org/10.1186/s40649-014-0003-2