Information diffusion and virus propagation are the fundamental processes often taking place in networks. The problem of devising a strategy to facilitate or block such process has received a considerable amount of attention. A major challenge therein is that the underlying network of diffusion is often hidden. Most researchers dealing with this issue assume only one underlying network over which cascades spread. However, in the real world, whether the transmission pathways of a contagion, a piece of information, emerge or not depends on many factors, such as the topic of the information and the time when the information is first mentioned. In our opinion, it is impractical to model the diffusion processes by using only a single network when information is of all kind and diffuses in different underlying topic-specific networks. In this paper, we formulate a problem of K-network inference, inferring K underlying diffusion networks, based on a proposed probabilistic generative mixture model that models the generation of cascades. We further propose an algorithm that could cluster similar cascades and infer the corresponding underlying network for each cluster in the Expectation-Maximization framework. Finally, in experiments, we show that our algorithm could cluster cascades and infer the underlying networks effectively.
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