论文标题
两部分网络的学位校正潜在模型的变异估计器
Variational Estimators of the Degree-corrected Latent Block Model for Bipartite Networks
论文作者
论文摘要
在各个科学和工程领域，双分部分的图形无处不在。同时将两种类型的节点分组在两部分图中，通过双分类代表了此类图的网络分析中的基本挑战。潜在块模型（LBM）是一种常用的基于模型的工具。但是，LBM的有效性通常受数据矩阵中的行和列总和的影响限制。为了解决此限制，我们介绍了学位校正的潜在块模型（DC-LBM），该模型占行的不同程度和列簇的不同程度，可显着提高现实世界数据集和模拟数据的性能。我们通过为M步骤中的参数估计而创建封闭形式的解决方案来开发有效的变分期望最大化算法。此外，我们证明了标签的一致性和DC-LBM下变化估计器的收敛速率，只要在图的大小增加时，预期的图密度就接近零。
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.
