{
  "abstract": "Archetypal Analysis (AA) represents observations as convex combinations of extremal data-driven profiles, yielding interpretable low-dimensional descriptions of complex datasets. Classical AA relies on a least-squares objective, which is poorly suited to discrete observations such as binary, count, and categorical data. We introduce an efficient likelihood-based framework for AA supporting Bernoulli, Poisson, and multinomial observation models. Our optimization scheme employs local quadratic approximations of the negative log-likelihood, enabling constrained updates through sequential minimal optimization (SMO) and an active-set method. Scalability is improved by bounding the active set while preserving simplex feasibility. We further introduce a cross-validated predictive likelihood criterion for selecting the number of archetypes, providing a principled alternative to reconstruction-error heuristics and stability-based diagnostics. Synthetic experiments demonstrate computational efficiency and accurate recovery of model complexity. Applications to single-cell RNA sequencing, microbiome composition, and somatic mutation data show that the learned archetypes capture interpretable domain-specific structures while achieving competitive likelihood fits and stable solutions. Overall, the proposed framework enables efficient likelihood-based archetypal analysis of discrete data, complemented by predictive likelihood-based model selection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12035",
  "author_total": 3,
  "authors": [
    {
      "name": "A. Emilie J. Wedenborg"
    },
    {
      "name": "Jesper Løve Hinrich"
    },
    {
      "name": "Morten Mørup"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wrj04v9b23gb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12035",
  "fulltext_url": null,
  "id": "2wrj04v9b23gb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12035",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Advanced Clustering Algorithms Research"
    ]
  ],
  "openalex": "W7221176764",
  "pdf_url": "https://arxiv.org/pdf/2610.12035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wrj04v9b23gb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:03Z",
      "native_id": "2610.12035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Efficient and Generalizable Archetypal Analysis for Discrete Data",
  "title_text": "Efficient and Generalizable Archetypal Analysis for Discrete Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/2wrj04v9b23gb",
  "venue": "arXiv",
  "versions": []
}