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Link prediction, i.e., predicting links or interactions between objects in a network, is an important task in network analysis. Although the problem has attracted much attention recently, there are several challenges that have not been addressed so far. First, most existing studies focus only on link prediction in homogeneous networks, where all objects and links belong to the same type. However, in the real world, heterogeneous networks that consist of multi-typed objects and relationships are ubiquitous. Second, most current studies only concern the problem of whether a link will appear in the future but seldom pay attention to the problem of when it will happen. In this paper, we address both issues and study the problem of predicting when a certain relationship will happen in the scenario of heterogeneous networks. First, we extend the link prediction problem to the relationship prediction problem, by systematically …