{
  "abstract": "Manifold fitting seeks to recover the geometric structure underlying noisy ambient observations. We propose Successive Tangent Space Projection (STSP), an iterative manifold-fitting method that reduces normal noise while preserving tangential variation. The former improves fitting accuracy, whereas the latter helps retain geometric coverage. We characterise the \\rev{nearby population fixed-point set} of STSP as a manifold-fitting object. Under uniform sampling from a compact smooth manifold with positive reach and isotropic Gaussian noise, this set lies within $O(σ^2)$ of the underlying manifold, and \\rev{nearby population orbits} converge geometrically to it. At the finite-sample level, with high probability, fixed points in the local tube lie within $O(σ^2)$ of the underlying manifold up to sampling error, and empirical orbits \\rev{initialised within that tube} and generated from a fixed reference sample enter and remain in the same neighbourhood. We further develop a multi-scale extension, MS-STSP, designed to reduce curvature bias while preserving the $O(σ^2)$ geometric localization order of STSP at both the population and finite-sample levels. Numerical experiments show that STSP compares favourably with competing methods in balancing fitting accuracy and geometric coverage, and that MS-STSP reduces curvature-induced shrinkage, particularly under high noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09423",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuqing Xia"
    },
    {
      "name": "Bingjie Li"
    },
    {
      "name": "Zhigang Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bgzstzrt4htx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09423",
  "fulltext_url": null,
  "id": "8bgzstzrt4htx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09423",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7221000807",
  "pdf_url": "https://arxiv.org/pdf/2610.09423",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bgzstzrt4htx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:48Z",
      "native_id": "2610.09423",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09423"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Manifold Fitting by Successive Tangent-Space Projection",
  "title_text": "Manifold Fitting by Successive Tangent-Space Projection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:48Z",
  "url": "https://research.draconitic.com/paper/8bgzstzrt4htx",
  "venue": "arXiv",
  "versions": []
}