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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.24556 [stat.ML]

(or arXiv:2609.24556v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.24556 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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