Identifying Representational Biases in Datasets Using PCA: A Max-Disparity Partition Framework

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.

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BibTeX

@misc{arjun2026identifying,
  title = {{Identifying Representational Biases in Datasets Using PCA: A Max-Disparity Partition Framework}},
  author = {Arjun KM and Shashi Jain},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24556},
  eprint = {2609.24556},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24556},
}

RIS

TY  - UNPB
TI  - Identifying Representational Biases in Datasets Using PCA: A Max-Disparity Partition Framework
AU  - Arjun KM
AU  - Shashi Jain
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24556
UR  - https://arxiv.org/abs/2609.24556
AB  - 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.
ER  -

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