Latent Factor Modeling of Large-Scale Directed Networks with Covariates and Structures

This proposed research project will develop a flexible latent factor framework for modeling large-scale directed networks with covariates and structures. The latent factor framework introduces two sets of latent factors to model the out-nodes and in-nodes separately in the directed networks. On this ground, a bi-directional community detection method is developed to detect two different sets of communities within the same set of nodes, one with similar following patterns, and the other with similar followers. Covariates can also be incorporated in the latent factor model through local smoothing to address the adapted homophily phenomenon for better edge prediction accuracy. The framework is further extended with network autoregression to allow time-evolving directed networks. The PI will investigate the theoretical properties of the proposed methods, and establish their asymptotic and finite-sample probability bounds. The PI will also develop efficient computing algorithms to facilitate large-scale optimization, integrating the strength of parallel computing platform. The proposed methods will be applied to model social networks consisting of millions of active users.