{
  "abstract": "Principal Component Analysis (PCA) minimises aggregate reconstruction error, which can inadvertently represent majority subgroups with substantially higher fidelity than minority subgroups. Fairness-aware extensions of PCA correct this disparity but require group labels as input. We address the logically prior question: given only a data matrix, which binary partition of the data suffers the greatest representational disparity under a shared PCA projection? We formalise this as the max-disparity partition problem and propose a greedy local-search algorithm, grounded in the Fiduccia-Mattheyses bipartitioning framework, that discovers the disparity-maximising partition without any predefined group labels. Two benchmark algorithms, a fixed-projection sorting baseline and a simulated-annealing variant, confirm that the greedy solution is empirically near-optimal. Having identified the partition, we attribute the disparity to specific features via PCA loading scores and association rule mining, enabling a practitioner to assess whether the disadvantaged group corresponds to a human-meaningful minority. On the Predict Students' Dropout and Academic Success dataset, representational disparity is driven predominantly by institutional and programmatic proxies for socioeconomic disadvantage, with gender emerging as a secondary but consistent contributor within the disadvantaged group. The discovered partition is then passed directly to Fair PCA, completing a detect-explain-mitigate pipeline.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24556",
  "author_total": 2,
  "authors": [
    {
      "name": "Arjun KM"
    },
    {
      "name": "Shashi Jain"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwp2ratrjmx7p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24556",
  "fulltext_url": null,
  "id": "bwp2ratrjmx7p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24556",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "3311|Ethics and Social Impacts of AI"
    ]
  ],
  "openalex": "W7214013427",
  "pdf_url": "https://arxiv.org/pdf/2609.24556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwp2ratrjmx7p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:33Z",
      "native_id": "2609.24556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Identifying Representational Biases in Datasets Using PCA: A Max-Disparity Partition Framework",
  "title_text": "Identifying Representational Biases in Datasets Using PCA: A Max-Disparity Partition Framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/bwp2ratrjmx7p",
  "venue": "arXiv",
  "versions": []
}