HMSL: Source localization based on higher-order Markov propagation

The widespread use of the Internet and social media has brought us great convenience, but it has also exposed us to a lot of false information and malicious attacks. It is vital to accurately locate the source of the harmful spread to prevent it from spreading further. Most previous studies have assumed that the propagation path is memoryless and always the shortest path. This assumption implies the first-order Markov property of propagation paths. This paper takes into account the higher-order Markov property of propagation paths in the source localization problem. Firstly, the problem of source localization based on observers is formulated. Then, we introduce the higher-order Markov property of propagation paths into the problem and propose a reaction–synchronization–diffusion model to model the propagation process on the higher-order network. On this basis, we build a framework named source localization based on higher-order Markov propagation (HMSL), which is compatible with traditional algorithms for source localization. After that, we conducted experiments on a real dataset and found that the HMSL has significant improvement in the source localization compared to the first-order network. Sensitivity analysis indicates that the degree of improvement is significantly influenced by the probability of infection and the proportion of higher-order nodes. Furthermore, we investigated the reason behind the improvement and found that the first-order network creates paths that do not exist within the raw data. When these fake paths are shorter than actual propagation paths, the length of propagation paths and estimated activation time of observers will be underestimated, thus decreasing the accuracy of source localization. The HMSL framework can solve this problem effectively.