Bipartite Structured Gaussian Graphical Modeling via Adjacency Spectral Priors

Learning a graph with a bipartite structure IS essential for interpretability and identification of the relationships among data in numerous applications including document clustering, network medicine, etc. To learn a bipartite structure is equivalent to a max-cut problem, which is an NP-hard problem. Existing methods employ a two-stage procedure and are computationally demanding as they require solving semi-definite programming. In this paper, we introduce a bipartite graph learning framework lying at the integration of Gaussian graphical models (GGM) and spectral graph theory. The proposed algorithms are provably convergent and practically amenable for large-scale unsupervised graph learning tasks. Numerical experiments demonstrate the effectiveness of the proposed algorithm over existing state-of-the-art methods. An R package containing code for all the experimental results is available at https://cran.r-project.org/package=spectralGraphTopology.