Automatic depth-based local center clustering via $\beta$-integrated local depth and adaptive grouping

Abstract: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 $\beta$-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.

Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2609.26748 [stat.ME]

(or arXiv:2609.26748v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2609.26748 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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