Joint Modeling of Hypergraph Networks for Community Detection and Graph Embedding

This proposed research project will develop a joint modelling framework for network embedding and community detection in hypergraph networks. It introduces a set of latent vectors to embed each node in the hypergraph network through tensor decomposition, and a novel regularization term on the latent vectors to detect community structures. The proposed framework can be adapted to both uniform and non-uniform hypergraph networks, and particularly, a new augmentation step is proposed to augment the non- uniform hypergraph networks into a special type of uniform multi-hypergraph networks. The framework is further extended to allow mixed community memberships in hypergraph 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 citation networks consisting of hyperedges with various cardinalities.