发表机构
University of Milano - Bicocca; University of Milano; University of Trento（米兰比可卡大学; 米兰大学; 特伦托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出融合模块化与持久性准则的Scaled-NAP质量函数族，开发Milano算法优化它，在基准与真实网络上验证其检测细粒度社区的有效性及高效性。
AI 中文摘要
社区检测方法必须平衡两个相互竞争的目标：识别小型、内聚的群组，同时避免过度碎片化。模块化是应用最广泛的优化准则，但由于其分辨率限制，通常会合并大型网络中的小型社区。相比之下，基于持久性的准则则会促进更细粒度的划分。我们提出缩放空调整持久性（Scaled Null-Adjusted Persistence，Scaled-NAP），这是一个参数化的质量函数族，融合了上述两种准则。该定义利用了一个集群的模块化贡献与其空调整持久性（Null-Adjusted Persistence，NAP）乘以其相对体积之间的精确恒等式。将该体积因子提升至参数α∈[0,1]，当α=0时得到NAP，当α=1时得到模块化，而中间值则控制检测到的划分的尺度。我们推导了合并两个社区可优化目标函数的条件，并表征了尺度依赖性的出现，包括在洞穴图（Caveman graphs）上的分辨率限制行为。我们开发了Milano算法，这是一种用于在大型网络上优化Scaled-NAP的多级Louvain式启发式算法。在加权和不加权的Lancichinetti-Fortunato-Radicchi基准上的实验表明，在可检测到真实结构的所有情况下，Scaled-NAP都能实现最高或并列最高的恢复性能，且在社区规模异质性下其优势会增强。对三个最多包含110万个节点的真实网络的测试证实，它具备识别细粒度真实社区的能力。Milano算法也是在大型网络上评估的方法中速度最快的。这些结果表明，Scaled-NAP为基于模块化和基于持久性的社区检测方法提供了一种有效且可扩展的桥梁。
英文摘要
Community detection methods must balance two competing objectives: identifying small, cohesive groups while avoiding excessive fragmentation. Modularity, the most widely adopted optimization criterion, typically merges small communities in large networks due to its resolution limit. In contrast, a persistence-based criterion promotes more granular partitions. We introduce Scaled Null-Adjusted Persistence (Scaled-NAP), a parametric family of quality functions that incorporates both these criteria. The definition exploits the exact identity between a cluster's modularity contribution and its Null-Adjusted Persistence (NAP) multiplied by its relative volume. Raising this volume factor to a parameter $α\in[0,1]$ yields NAP at $α=0$ and modularity at $α=1$, while intermediate values control the scale of the detected partition. We derive conditions under which merging two communities improves the objective function and characterize the emergence of scale dependence, including resolution-limit behaviour on Caveman graphs. We develop the Milano algorithm, a multilevel Louvain-style heuristic for optimizing Scaled-NAP on large networks. Experiments on weighted and unweighted Lancichinetti-Fortunato-Radicchi benchmarks show that Scaled-NAP achieves the highest or tied-highest recovery wherever the ground truth structure is detectable, with its advantage increasing under community-size heterogeneity. Tests on three real networks with up to 1.1 million nodes confirm its capability to identify fine-grained ground-truth communities. The Milano algorithm also turned out to be the fastest method evaluated on large networks. These results show that Scaled-NAP provides an effective and scalable bridge between modularity-based and persistence-based community detection methodologies.
