arXiv:2509.03834cs.LGcs.AI2025-09被引 4

将社区检测建模为博弈,提升效率与鲁棒性。

From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game

  • 把陈氏模型转为局部收益博弈,实现快速收敛。
  • 提出双标准稳定性,控制分辨率提升检测精度。
  • 适合需要高精度社区识别的研究者使用。

社区检测是数据科学中的基础问题,旨在将节点划分为互不重叠的群体。本文从博弈论视角重新审视常数陈氏模型(CPM),强调其高效性、鲁棒性和准确性。效率方面:通过将全局哈密顿量分解为局部效用函数,将CPM重构为潜在效用型享乐博弈,证明基于更好响应动态的局部优化可在伪多项式时间内收敛至均衡划分。鲁棒性方面:引入两种稳定性标准——一种严格标准要求节点同时最大化社区内邻居、最小化非邻居;另一种宽松标准采用加权和形式,由分辨率参数调控。准确性方面:在社区追踪场景中,利用部分真实标签启动莱登算法,实验表明具有鲁棒性的划分能更准确恢复真实社区结构。

原文摘要 · Abstract (English)

Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.

社区检测博弈论网络分析

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