Mining Spatio-temporal Surveillance Network Based On Group Sparse Bayesian Learning

There are a variety of diffusion systems in the real world, such as epidemic spreading systems and information diffusion systems. In order to understand the complex mechanisms of these diffusion process, researchers began to study the prediction in diffusion system. In short, the prediction of diffusion system means: according to the current observed system state, we can predict the system status of next time which is unknown.So far, the existing prediction methods are based on the following two assumptions:(1) Diffusion network structure which depends spreading process is known;(2) Without considering the costs of monitoring, we think the status of all nodes in diffusion networks can be accessed. However, these two assumptions are often difficult to set up in practice. On the one hand, diffusion process in real world is complex. Interactive structure in the nodes of diffusion network is often heterogeneous, hidden, dynamic and cannot be directly observed. So the specific diffusion network structure is usually difficult to obtain; On the other hand, diffusion process in real world tend to cover larger spatial and temporal scales. Such as the diffusion of information on the Internet and the spread of epidemics. So real-time monitoring of all network nodes has a huge cost. Especially under the conditions of very limited monitoring resources, the monitoring of all diffusion space is particularly difficult.In response to these two problems, we propose the concept of spatio-temporal surveillance network and give a method of mining spatio-temporal surveillance network from data. This article will define a spatio-temporal surveillance network which is similar to a real diffusion hidden networks. The topology has the following characteristics:(1) The network is a directed network, whose directed edges represent influence relations between nodes in the diffusion process;(2) the network contains all the nodes of real diffusion networks;(3) There are a small number of sentinel nodes in the network. Based on the current status of the sentinel nodes, we can predicted the status of all network nodes approximately at next time.Based on the above concepts, this article propose two spatio-temporal surveillance network learning methods, which aim at two common types of diffusion systems.(1) For linear diffusion system(node state indicates a continuous real number), this article give a linear regression problem for spatio-temporal surveillance network learning, and propose a method of mining spatio-temporal surveillance network with regression in group sparse bayesian learning.(2) For nonlinear diffusion system with sparse spreading data(node status is represented as a discrete integer), this article give a nonlinear classification problem for spatiotemporal surveillance network learning, and propose a method of mining spatio-temporal surveillance network with classification in group sparse bayesian learning.Finally, based on a variety of experimental program, the efficacy of the GSBL algorithm and the GSBN algorithm is theoretically analyzed and validated empirically in both synthetic and real-world data.