# Automatic depth-based local center clustering via β-integrated local depth and adaptive grouping

arXiv: https://arxiv.org/abs/2609.26748 · HTML: https://mlsanity.com/paper/2609.26748/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 56 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 10 of 10)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Efficient Parameter-free Clustering Using First Neighbor Relations](https://mlsanity.com/paper/1902.11266/) (2019)
- [DinoSR: Self-Distillation and Online Clustering for Self-supervised Speech Representation Learning](https://mlsanity.com/paper/2305.10005/) (2023)
- [Choosing among notions of multivariate depth statistics](https://mlsanity.com/paper/2004.01927/) (2020)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [Measuring the Validity of Clustering Validation Datasets](https://mlsanity.com/paper/2503.01097/) (2025)
- [A Distributed and Approximated Nearest Neighbors Algorithm for an Efficient Large Scale Mean Shift Clustering](https://mlsanity.com/paper/1902.03833/) (2019)
- [K*-Means: A Parameter-free Clustering Algorithm](https://mlsanity.com/paper/2505.11904/) (2025)
- [Depth-Based Local Center Clustering: A Framework for Handling Different Clustering Scenarios](https://mlsanity.com/paper/2505.09516/) (2025)
- [β-integrated local depth and corresponding partitioned local depth representation](https://mlsanity.com/paper/2506.14108/) (2025)

## Abstract (arXiv)

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.