Source localization has attracted increasing attention in recent years due to its vital role in governing the harmful propagation. However, existing localization methods do not fully consider the temporal characteristics in propagation and struggle to leverage the continuous-time information of real-world propagation scenarios. Moreover, the aggregation ability of GNN based localization models is limited by the structural noise commonly present in complicated real-world topologies. To address these challenges, a Spectral Neural Ordinary Differential Equation (SNODE) is proposed to infer the source in real-world continuous-time scenarios. First, the forward propagation is formulated as a flow based ODE system, and the source localization problem is transformed into an inverse ODE modeling task. Second, a neural process based on a graph variational autoencoder is introduced to encode global latent propagation patterns as a conditioning variable for the ODE system. Third, a spectral graph optimization is performed to suppress topological noise by filtering out high-frequency components that degrade the quality of graph aggregation in the neural process. Comprehensive experiments demonstrate that SNODE not only outperforms the optimal baseline in real-world continuous-time propagation scenarios with an average performance improvement of 43.8%, but also achieves consistently superior performance in synthetic discrete-time datasets with an improvement of 4.5%, highlighting its strong generalization ability in different propagation settings. Our code is available at https://github.com/cgao-comp/SNODE.

Source localization in social platforms is critical for managing and controlling the misinformation spreading. Despite all the recent advancements, existing methods do not consider the dynamic and heterogeneous propagation behaviors of users and are developed based on simulated data with strong model assumptions, limiting the application in real-world scenarios. This research addresses this limitation by presenting a novel framework for source localization, grounded in real-world propagation cascades from platforms like Weibo and Twitter. What's more, recognizing the user-driven nature of users in information spread, we systematically crawl and integrate user-specific profiles, offering a realistic understanding of user-driven propagation dynamics. In summary, by developing datasets derived from real-world propagation cascades, we set a precedent in enhancing the authenticity and practice of source identification for social media. Our comprehensive experiments not only validate the feasibility and rationale of our novel user-centric localization approaches but also emphasize the significance of considering user profiles in real-world propagation scenarios. The code is available at https://github.com/cgao-comp/NFSL.

The topology of diffusion networks plays an essential role in understanding information propagation dynamics and conducting social network analysis. However, diffusion networks are often unobservable in practical applications, leading to wide research on network inference from information cascades over the past decade. At present, novel cascades-based methods have been further developed to recover temporal dynamics and network topology by exploring the utilization of node temporal information, resulting in notable advancements. However, it requires high costs to acquire extensive temporal information, and the performance of network inference may decrease due to potential observational errors. Therefore, this paper specifically focuses on the time-independent scenario to address these limitations. Firstly, this paper models the node statuses of each diffusion process by leveraging the assumption of propagation trees based on the well-known independent cascade model. Subsequently, a gradient-based approach is developed to estimate the influences between nodes, facilitating the inference of network structure. Furthermore, this paper proposes a Monte Carlo EM-based approach to enhance the efficiency of network inference while maintaining comparable accuracy. Extensive experiments are conducted to verify the efficiency and effectiveness of our approaches on both synthetic and real-world networks.

The rapid diffusion of hazardous information in large-flow-based social media causes great economic losses and potential threats to society. It is crucial to infer the inner information source as early as possible to prevent further losses. However, existing localization methods wait until all deployed sensors obtain propagation information before starting source inference within a network, and hence the best opportunity to control propagation is missed. In this paper, we propose a new localization strategy based on finite deployed sensors, named Greedy-coverage-based Rapid Source Localization (GRSL), to rapidly, flexibly and accurately infer the source in the early propagation stage of large-scale networks. There are two phases in GRSL. In the first phase, the Greedy-based Strategy (GS) greedily deploys sensors to rapidly achieve wide area coverage at a low cost. In the second phase, when a propagation event within a network is observed by a part of the sensors, the Inference Strategy (IS) with an earlier response mechanism begins executing the source inference task in an earlier small infected area. Comprehensive experiments with the SOTA methods demonstrate the superior performance and robustness of GRSL in various application scenarios.

Recently, the rapid diffusion of malicious information in online social networks causes great harm to our society. Therefore, it is of great significance to localize diffusion sources as early as possible to stem the spread of malicious information. This paper proposes a novel sensor-based method, called greedy full-order neighbor localization (denoted as GFNL), to solve this problem under a low infection propagation in line with the real world. More specifically, GFNL includes two main components, i.e., the greedy-based sensor deployment strategy (DS) and direction-path-based source estimation strategy (ES). In more detail, to ensure sensors can observe a propagation information as early as possible, a set of sensors is deployed in a network to minimize the geodesic distance (i.e., the distance of the shortest path) between the candidate set and the sensor set based on DS. Then when a fraction of sensors observe a propagation, ES infers the source based on the idea that the distance of the actual propagation path is proportional to the observed time. Compared with some state-of-the-art methods, comprehensive experiments have proved the superiority and robustness of our proposed GFNL.