Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks

TL;DR

This paper introduces a degree-corrected latent block model for bipartite networks, improving biclustering accuracy by accounting for degree heterogeneity, and develops an efficient variational EM algorithm with proven consistency.

Contribution

The paper proposes the DC-LBM for better biclustering of bipartite graphs, along with a scalable variational EM algorithm and theoretical guarantees.

Findings

Enhanced performance on real-world and simulated data

Efficient variational EM algorithm with closed-form solutions

Proven label consistency and convergence rates

Abstract

Bipartite graphs are ubiquitous across various scientific and engineering fields. Simultaneously grouping the two types of nodes in a bipartite graph via biclustering represents a fundamental challenge in network analysis for such graphs. The latent block model (LBM) is a commonly used model-based tool for biclustering. However, the effectiveness of the LBM is often limited by the influence of row and column sums in the data matrix. To address this limitation, we introduce the degree-corrected latent block model (DC-LBM), which accounts for the varying degrees in row and column clusters, significantly enhancing performance on real-world data sets and simulated data. We develop an efficient variational expectation-maximization algorithm by creating closed-form solutions for parameter estimates in the M steps. Furthermore, we prove the label consistency and the rate of convergence of the variational estimator under the DC-LBM, allowing the expected graph density to approach zero as long as the average expected degrees of rows and columns approach infinity when the size of the graph increases.