{
  "abstract": "One of the earliest techniques in multivariate analysis, Principal Component Analysis (PCA) remains among the most popular ones in the area. PCA, however, is a linear and bidirectional technique (principal directions $\\pm\\mathbf{u}$ are defined up to a sign), which is fine under Gaussian or elliptical assumptions but constitutes a major limitation outside that restrictive context. This has prompted the development of numerous nonlinear approaches. We show here how recent results in measure transportation allow for a nonlinear and strictly directional (disentangling $\\mathbf{u}$ and $-\\mathbf{u}$) concept preserving the intuitive interpretation of the classical linear concept by maximizing expected squared arc lengths along data-driven principal curves rather than principal directions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02158",
  "author_total": 3,
  "authors": [
    {
      "name": "Marc Hallin"
    },
    {
      "name": "Klaus Nordhausen"
    },
    {
      "name": "Una Radojicic"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fv904n8dmmmz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02158",
  "fulltext_url": null,
  "id": "8fv904n8dmmmz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02158",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02158",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fv904n8dmmmz.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02158",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02158"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Directional Nonlinear Principal Components: a measure transportation approach",
  "title_text": "Directional Nonlinear Principal Components: a measure transportation approach",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/8fv904n8dmmmz",
  "venue": "arXiv",
  "versions": []
}