The problem of community detection in multi-layer undirected networks has received considerable attention in recent years. However, practical scenarios often involve multi-layer bipartite networks, where each layer consists of two distinct types of nodes. Existing community detection algorithms tailored for multi-layer undirected networks are not directly applicable to multi-layer bipartite networks. To address this challenge, this paper introduces a novel multi-layer degree-corrected stochastic co-block model specifically designed to capture the underlying community structure within multi-layer bipartite networks. Within this framework, we propose an efficient debiased spectral co-clustering algorithm for detecting nodes' communities. We establish the consistent estimation property of our proposed algorithm and demonstrate that an increased number of layers in bipartite networks improves the accuracy of community detection. Through extensive numerical experiments, we showcase the superior performance of our algorithm compared to existing methods. Additionally, we validate our algorithm by applying it to real-world multi-layer network datasets, yielding meaningful and insightful results.

翻译：近年来，多层无向网络中的社区检测问题已受到广泛关注。然而，实际场景中常涉及多层二分网络，其中每一层由两类不同类型的节点组成。现有针对多层无向网络设计的社区检测算法无法直接适用于多层二分网络。为解决这一挑战，本文提出了一种新颖的多层度数修正随机共块模型，该模型专门用于捕捉多层二分网络中的潜在社区结构。在此框架下，我们提出了一种高效的偏差校正谱共聚类算法来检测节点的社区。我们建立了所提算法的一致性估计性质，并证明二分网络中层数的增加能提升社区检测的准确性。通过大量数值实验，我们展示了该算法相较于现有方法的优越性能。此外，我们将算法应用于真实多层网络数据集，获得了有意义且富有洞见的结果。