{
  "abstract": "This paper introduces a principal component analysis ( \\(\\Phi _\\alpha\\) -PCA) in a topological structure called \\(\\Phi _\\alpha\\) -linear spaces. The \\(\\Phi _\\alpha\\) -PCA consists in an isomorphic deformation of the usual PCA through a hyperparameter \\(\\alpha\\) . It is shown that the statistics employed in standard PCA (cosines and correlations) exist in \\(\\Phi _\\alpha\\) -linear spaces, these are U -statistics. As the regular PCA is a special case of \\(\\Phi _\\alpha\\) -PCA when \\(\\alpha = 1\\) , simulations and applications on images are provided to outline the relevance of the \\(\\Phi _\\alpha\\) -PCA in various settings and specifically in the presence of noise and outliers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Cassandra Mussard"
    },
    {
      "name": "Walter Briec"
    },
    {
      "name": "Charles Condevaux"
    },
    {
      "name": "Stéphane Mussard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4585jv7tb7kf9.bib",
  "cited_by": 0,
  "doi": "10.1186/s40537-026-01473-x",
  "fulltext_url": null,
  "id": "4585jv7tb7kf9",
  "issns": [
    "2196-1115"
  ],
  "landing_url": "https://hal.science/hal-05780128v1",
  "language": "en",
  "licence": "CC-BY-NC-ND",
  "licence_label": "CC BY-NC-ND",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.stat"
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    [
      "openalex",
      "2613|Statistical Methods and Applications"
    ]
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  "openalex": "W7162249257",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-24",
  "publisher": "Springer",
  "ris": "https://research.draconitic.com/paper/4585jv7tb7kf9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "hal-05780128",
      "source": "hal",
      "url": "https://hal.science/hal-05780128v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "Principal component analysis in $$\\Phi _\\alpha$$-linear spaces",
  "title_text": "Principal component analysis in Φ _α-linear spaces",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/4585jv7tb7kf9",
  "venue": "Journal of Big Data",
  "versions": []
}