A-DLCC: Automatic Depth-Based Local Center Clustering via β-Integrated Local Depth
Field: Machine Learning Authors: Siyi Wang, Alexandre Leblanc, Paul D. McNicholas Published: 2026-09-22 arXiv: 2609.26748
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.
Key Points
- No parameter tuning: A-DLCC is fully data-driven and does not require users to specify the number of clusters or neighborhood size.
- β-integrated local depth: Identifies stable exemplars (local centers) that remain central across multiple locality levels, ranked by representativeness.
- Group-level local similarity: A new nonparametric metric measures similarity between groups induced by local centers.
- Graph-theoretic merging: An adaptive criterion based on bottleneck paths—groups are absorbed by better-reached neighbors or bonded to mutually more-reachable neighbors.
- Statistical significance check: Every merge must be carried by a contact stronger than a configuration-model null hypothesis expects.
- Automatic stopping: The rule estimates the number of clusters and decides when to stop merging.
- Validation: Experiments on synthetic and real datasets demonstrate interpretable clustering without tuning.