Inside the atoms: ranking on a network of networks

Networks are prevalent and have posed many fascinating research questions. How can we spot similar users, e.g., virtual identical twins, in Cleveland for a New Yorker? Given a query disease, how can we prioritize its candidate genes by incorporating the tissue-specific protein interaction networks of those similar diseases? In most, if not all, of the existing network ranking methods, the nodes are the ranking objects with the finest granularity. In this paper, we propose a new network data model, a Network of Networks (NoN), where each node of the main network itself can be further represented as another (domain-specific) network. This new data model enables to compare the nodes in a broader context and rank them at a finer granularity. Moreover, such an NoN model enables much more efficient search when the ranking targets reside in a certain domain-specific network. We formulate ranking on NoN as a regularized optimization problem; propose efficient algorithms and provide theoretical analysis, such as optimality, convergence, complexity and equivalence. Extensive experimental evaluations demonstrate the effectiveness and the efficiency of our methods.