Inferring the source of diffusion in networks under weak observation condition

Diffusion source inference in a fast and accurate way is of much importance for the control of the information spreading in networks. Typical models usually assume the infection times of the vertices in the observation set to be available, whereas it is sometimes difficult to observe the exact times because of the status invisibility of some vertices. In this paper, we propose a weak observation condition that requires merely the infection orders of the observers in a network. Under the weak observation condition, a statistical inference model based on the Monte Carlo sampling (MCS) method is further proposed to infer the real diffusion source from the source candidate set by evaluating the order correlation coefficient between the sampled infection sequence and the observed infection sequence. Experiments are worked out with both synthetic and real-world networks to show the effectiveness and availability of our method.