[论文] [论文] Automatic depth-based local center clustering via $β$-integr...

论文概要

研究领域: ML 作者: Siyi Wang, Alexandre Leblanc, Paul D. McNicholas 发布时间: 2026-09-22 arXiv: 2609.26748

中文摘要

聚类把无标签数据分组，多数方法需用户指定聚类数或邻域大小等参数。我们提出 A-DLCC——完全数据驱动、免数值调参的自动基于深度的局部中心聚类。用 β 积分局部深度识别稳定范例点：在多个局部层次持续居中的"局部中心"，按代表性排序；每个局部中心诱导一组相似点，组级相似度由非参数度量"组级局部相似度"衡量。合并引导引入图论瓶颈路径思想：一个组要么被它"到达效果优于自身"的邻居吸收，要么与双方都发现比各自背景更易达的邻居结合；每次合并须由比配置模型零假设预期更强的联系承载。规则自动估计聚类数并决定何时停止。合成与真实数据实验表明，A-DLCC 免调参即可产出可解释的聚类结果。

原文摘要

Clustering is an unsupervised learning technique that partitions unlabeled data into groups. Most existing methods require user-specified parameters, such as the number of clusters or neighborhood size. Conversely, we propose automatic depth-based local center clustering (A-DLCC), a fully data-driven method that eliminates numerical parameter tuning. A-DLCC uses the \(β\)-integrated local depth to identify stable exemplars, points consistently central across multiple locality levels, termed local centers, which are ranked by their representativeness. Each local center induces a group of similar points, with group-level similarity measured by a proposed nonparametric metric called group-level local similarity. To guide merging, we incorporate the bottleneck path idea from graph theory, which forms the basis of our adaptive merging criterion. Based on this criterion, we design a single agglomeration rule in which a group is either absorbed by a neighbor it reaches better than itself or bonded to a neighbor that both sides find more reachable than their own background, every merge being additionally required to be carried by a contact stronger than a configuration-model null expects. The rule automatically estimates the number of clusters and decides when to stop merging. Experiments on synthetic and real data show that A-DLCC produces interpretable clustering results without parameter tuning.

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*自动采集于 2026-09-24*

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