{
  "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 $β$-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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26748",
  "author_total": 3,
  "authors": [
    {
      "name": "Siyi Wang"
    },
    {
      "name": "Alexandre Leblanc"
    },
    {
      "name": "Paul D. McNicholas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8x9dznmcek2pr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26748",
  "fulltext_url": null,
  "id": "8x9dznmcek2pr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26748",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Advanced Clustering Algorithms Research"
    ]
  ],
  "openalex": "W7214105541",
  "pdf_url": "https://arxiv.org/pdf/2609.26748",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8x9dznmcek2pr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:49Z",
      "native_id": "2609.26748",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26748"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Automatic depth-based local center clustering via $β$-integrated local depth and adaptive grouping",
  "title_text": "Automatic depth-based local center clustering via β-integrated local depth and adaptive grouping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:49Z",
  "url": "https://research.draconitic.com/paper/8x9dznmcek2pr",
  "venue": "arXiv",
  "versions": []
}