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The increasingly connected world has catalyzed the fusion of networks from different domains, which facilitates the emergence of a new network model-multi-layered networks. Examples of such kind of network systems include critical infrastructure networks, biological systems, organization-level collaborations, cross-platform e-commerce, and so forth. One crucial structure that distances multi-layered network from other network models is its cross-layer dependency, which describes the associations between the nodes from different layers. Needless to say, the cross-layer dependency in the network plays an essential role in many data mining applications like system robustness analysis and complex network control. However, it remains a daunting task to know the exact dependency relationships due to noise, limited accessibility, and so forth. In this article, we tackle the cross-layer dependency inference problem by modeling it as a collective collaborative filtering problem. Based on this idea, we propose an effective algorithm Fascinate that can reveal unobserved dependencies with linear complexity. Moreover, we derive Fascinate-ZERO, an online variant of Fascinate that can respond to a newly added node timely by checking its neighborhood dependencies. We perform extensive evaluations on real datasets to substantiate the superiority of our proposed approaches.

Cross-Dependency Inference in Multi-Layered Networks