{
  "abstract": "We propose to model singular data clouds by subanalytic sets, and develop an approach to semi-supervised learning in this setting. It relies on a Morrey-type embedding for Sobolev spaces relative to globally subanalytic measures with possibly singular support. As an illustration, we present a greedy method based on a Monte Carlo approximation of the Sobolev norm of the candidate solutions. We report numerical experiments on point clouds sampled from real algebraic varieties, as well as a test on a classification problem based on MNIST images downsampled into $7\\times7$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25450",
  "author_total": 1,
  "authors": [
    {
      "name": "Guillaume Valette"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2s0snjqmxhjr5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25450",
  "fulltext_url": null,
  "id": "2s0snjqmxhjr5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25450",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.AG"
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      "arxiv",
      "math.ST"
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      "arxiv",
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      "openalex",
      "1702|Machine Learning and Algorithms"
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  "openalex": "W7223019974",
  "pdf_url": "https://arxiv.org/pdf/2610.25450",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2s0snjqmxhjr5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25450",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25450"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Semi-supervised learning on singular data sets",
  "title_text": "Semi-supervised learning on singular data sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/2s0snjqmxhjr5",
  "venue": "arXiv",
  "versions": []
}