提出可微分三部图模块度，实现异构图的端到端聚类。
Differentiable Tripartite Modularity for Clustering Heterogeneous Graphs
- 基于加权共路径定义三部图社区结构，避免高阶张量计算。
- 在真实城市地籍数据上实现稳定收敛与空间一致的聚类结果。
- 适合处理多类型实体交互的异构图无监督聚类任务。
异构关系数据的聚类仍是图学习中的核心挑战，尤其当交互涉及超过两种实体类型时。尽管可微分模块度方法（如 DMoN）已实现同质图和二部图的端到端社区发现，但将其扩展至高阶关系结构仍不简单。本文提出一种针对三类节点通过中介交互构成的图的可微分三部图模块度形式。社区结构基于三部图中的加权共路径定义，并采用精确因子分解计算，避免了密集三阶张量的显式构建。在枢纽节点引入结构归一化以控制极端度异质性，确保优化稳定。所提目标可与图神经网络联合优化，保持边数线性的复杂度。在大规模城市地籍数据上验证，该框架展现出稳健的收敛性并生成空间一致的划分结果。这些成果表明，可微分三部图模块度是一种通用的异构图无监督聚类方法基础组件。
原文摘要 · Abstract (English)
Clustering heterogeneous relational data remains a central challenge in graph learning, particularly when interactions involve more than two types of entities. While differentiable modularity objectives such as DMoN have enabled end-to-end community detection on homogeneous and bipartite graphs, extending these approaches to higher-order relational structures remains non-trivial. In this work, we introduce a differentiable formulation of tripartite modularity for graphs composed of three node types connected through mediated interactions. Community structure is defined in terms of weighted co-paths across the tripartite graph, together with an exact factorized computation that avoids the explicit construction of dense third-order tensors. A structural normalization at pivot nodes is introduced to control extreme degree heterogeneity and ensure stable optimization. The resulting objective can be optimized jointly with a graph neural network in an end-to-end manner, while retaining linear complexity in the number of edges. We validate the proposed framework on large-scale urban cadastral data, where it exhibits robust convergence behavior and produces spatially coherent partitions. These results highlight differentiable tripartite modularity as a generic methodological building block for unsupervised clustering of heterogeneous graphs.
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