几何社区检测中的无离散化精确恢复
Discretization-free exact recovery in geometric community detection
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中文总结 AI 辅助
针对几何社区检测中现有方法需离散化空间的局限，提出一种直接作用于连续几何的GHCM无离散化多项式时间精确恢复算法，在更弱条件下实现精确恢复且实验表现超出理论保证范围。
中文摘要 AI 辅助
几何社区检测旨在恢复网络中的潜在社区，其连接性同时依赖于社区结构和连续空间几何。现有精确恢复方法通常会对基础空间进行离散化，这可能对连接函数施加限制性结构假设。我们针对几何隐藏社区模型（GHCM）开发了一种多项式时间、无离散化的精确恢复算法，可直接在连续几何上运行。即使连接函数在其可见范围的非平凡部分重合，且两个社区仅能通过它们与第三个社区的连接性来区分，我们的方法仍能成功。我们在这些更弱的条件下证明了精确恢复，并提供实验表明该算法在理论保证的范围之外也能成功。
英文摘要
Geometric community detection seeks to recover latent communities in networks where connectivity depends jointly on community structure and continuous spatial geometry. Existing exact-recovery approaches typically discretize the underlying space, which can impose restrictive structural assumptions on the connectivity functions. We develop a polynomial-time, discretization-free algorithm for exact recovery in the Geometric Hidden Community Model (GHCM), operating directly on the continuous geometry. Our method succeeds even when connectivity functions coincide on a nontrivial portion of their visibility range and when two communities can be distinguished only through their connectivity to a third community. We prove exact recovery under these weaker conditions and provide experiments showing that the algorithm succeeds beyond the theoretically guaranteed regime.
发表机构
- Leiden University（莱顿大学）
- Institut de Mathématiques Toulouse（图卢兹数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
