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Bibliographic Details
Main Authors: Zhao, Yunpeng, Hao, Ning, Zhu, Ji
Format: Preprint
Published: 2022
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Online Access:https://arxiv.org/abs/2206.08465
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author Zhao, Yunpeng
Hao, Ning
Zhu, Ji
author_facet Zhao, Yunpeng
Hao, Ning
Zhu, Ji
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2206_08465
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks
Zhao, Yunpeng
Hao, Ning
Zhu, Ji
Machine Learning
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.
title Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks
topic Machine Learning
url https://arxiv.org/abs/2206.08465