面向有向网络与二部网络的双向节点流行度模型
Two-way Node Popularity Model for Directed and Bipartite Networks
AI总结：
针对有向与二部网络社区检测未考虑节点流行度的问题，提出TNPM概率框架、DOM拟合方法与TSDC大规模算法，兼具精度与效率，可应用于真实网络分析。
摘要：
目前已有大量针对有向网络和二部网络中社区检测的研究，但这些研究往往未考虑节点在不同社区中的流行度，而这是现实网络中的普遍现象。为解决该问题，我们提出了一种名为双向节点流行度模型（Two-Way Node Popularity Model, TNPM）的新型概率框架，该框架还可适配广义次高斯族内不同分布的边。我们引入了删一法（Delete-One-Method, DOM）用于模型拟合与社区结构识别，并借助处理次高斯泛化的全新技术手段提供了全面的理论分析。此外，我们提出两阶段分块余弦算法（Two-Stage Divided Cosine Algorithm, TSDC）以更高效地处理大规模网络。大量数值研究表明，我们提出的方法在估计精度和计算效率方面具有多重优势。我们将方法应用于两个真实场景，发现了有价值的结果。
英文摘要：
There has been extensive research on community detection in directed and bipartite networks. However, these studies often fail to consider the popularity of nodes in different communities, which is a common phenomenon in real-world networks. To address this issue, we propose a new probabilistic framework called the Two-Way Node Popularity Model (TNPM). The TNPM also accommodates edges from different distributions within a general sub-Gaussian family. We introduce the Delete-One-Method (DOM) for model fitting and community structure identification, and provide a comprehensive theoretical analysis with novel technical skills dealing with sub-Gaussian generalization. Additionally, we propose the Two-Stage Divided Cosine Algorithm (TSDC) to handle large-scale networks more efficiently. Our proposed methods offer multi-folded advantages in terms of estimation accuracy and computational efficiency, as demonstrated through extensive numerical studies. We apply our methods to two real-world applications, uncovering interesting findings.
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