发表机构
Chongqing University of Technology（重庆理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对二部网络中的社区检测问题，提出基于对角删除Gram矩阵的谱聚类算法，证明其在温和条件下可实现精确恢复，并扩展到度校正模型，实验验证了理论结果。
AI 中文摘要
社区检测是二部网络中的一个基本问题，在现代数据分析中具有重要应用，包括推荐系统、生物网络和社会网络分析。与传统的单部图不同，二部网络由两种不同类型的节点组成，边仅连接不同类型的节点，因此恢复潜在社区需要估计两种节点类型上的标签。随机共块模型是此类网络的经典概率框架，然而在该设置下精确社区恢复的理论保证仍然有限，尤其是当社区数量增长、社区规模不均衡或节点度异构时。在本工作中，我们证明了基于对角删除的Gram矩阵的简单谱聚类算法，在稀疏性、社区平衡性和聚类数量的温和条件下，能够以高概率实现精确恢复。我们进一步将结果扩展到度校正的随机共块模型，其中每个节点携带其自身的度异质性参数，并表明该算法的行归一化版本保持了精确恢复的保证。大量实验验证了我们的理论发现。
英文摘要
Community detection in bipartite networks is a fundamental problem in modern data analysis, with applications in recommendation systems, biological networks, and social network analysis. Unlike conventional unipartite graphs, bipartite networks consist of two distinct types of nodes with edges only connecting across types, so recovering latent communities requires estimating labels on the two node types. The stochastic co-blockmodel is a classical probabilistic framework for such networks, yet theoretical guarantees for exact community recovery in this setting remain limited, especially when the number of communities grows, the community sizes are unbalanced, or the degrees are heterogeneous. In this work, we prove that a simple spectral clustering algorithm based on the diagonal-deleted Gram matrix achieves exact recovery with high probability under mild conditions on sparsity, community balance, and the number of clusters. We further extend the result to the degree-corrected stochastic co-blockmodel, where each node carries its own degree heterogeneity parameter, and show that a row-normalized version of the same algorithm maintains the exact recovery guarantee. Extensive experiments validate our theoretical findings.
Comments39 pages, 4 figures
