Community detection for weighted bipartite networks
This work addresses a gap in network analysis for weighted bipartite data, which is incremental as it extends prior binary models to handle edge weights without specific distributional requirements.
The authors tackled the problem of community detection in weighted bipartite networks, which existing models like Stochastic co-Blockmodel (ScBM) ignore, by introducing a Bipartite Distribution-Free model that relaxes distribution assumptions and accounts for node degree variation, resulting in spectral algorithms with theoretical guarantees for consistent node label estimation.
The bipartite network appears in various areas, such as biology, sociology, physiology, and computer science. \cite{rohe2016co} proposed Stochastic co-Blockmodel (ScBM) as a tool for detecting community structure of binary bipartite graph data in network studies. However, ScBM completely ignores edge weight and is unable to explain the block structure of a weighted bipartite network. Here, to model a weighted bipartite network, we introduce a Bipartite Distribution-Free model by releasing ScBM's distribution restriction. We also build an extension of the proposed model by considering the variation of node degree. Our models do not require a specific distribution on generating elements of the adjacency matrix but only a block structure on the expected adjacency matrix. Spectral algorithms with theoretical guarantees on the consistent estimation of node labels are presented to identify communities. Our proposed methods are illustrated by simulated and empirical examples.