Overlapping and nonoverlapping models

11/02/2021

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by   Huan Qing, et al.

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Consider a directed network with K_r row communities and K_c column communities. Previous works found that modeling directed networks in which all nodes have overlapping property requires K_r=K_c for identifiability. In this paper, we propose an overlapping and nonoverlapping model to study directed networks in which row nodes have overlapping property while column nodes do not. The proposed model is identifiable when K_r≤ K_c. Meanwhile, we provide one identifiable model as extension of ONM to model directed networks with variation in node degree. Two spectral algorithms with theoretical guarantee on consistent estimations are designed to fit the models. A small scale of numerical studies are used to illustrate the algorithms.