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<p>Principal Component Analysis (PCA) is a foundational technique in machine learning for reducing the dimensionality of high-dimensional datasets. However, PCA can lead to biased representations that disadvantage certain subgroups within the data. To address this issue, a Fair PCA (FPCA) model was introduced to equalize the reconstruction loss between subgroups, but the existing semidefinite relaxation (SDR) based approach is computationally expensive even for a suboptimal solution. Although several alternative FPCA variants have been developed to improve efficiency, they often shift attention away from equalizing the reconstruction loss – the central goal of FPCA. In this paper, we identify a hidden convexity in FPCA and introduce a new algorithm that solves the resulting convex optimization via an eigenvalue optimization. Our approach achieves the desired fairness in reconstruction loss without sacrificing performance. Experiments on real-world datasets show that the proposed FPCA algorithm is approximately <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(8\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>8</mn> <mo>×</mo> </mrow> </math></EquationSource> </InlineEquation> faster than the SDR-based algorithm while being at most 85% slower than standard PCA.</p>

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Fair principal component analysis via eigenvalue optimization

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Junhui Shen,
  • Aaron Davis,
  • Ding Lu,
  • Zhaojun Bai

摘要

Principal Component Analysis (PCA) is a foundational technique in machine learning for reducing the dimensionality of high-dimensional datasets. However, PCA can lead to biased representations that disadvantage certain subgroups within the data. To address this issue, a Fair PCA (FPCA) model was introduced to equalize the reconstruction loss between subgroups, but the existing semidefinite relaxation (SDR) based approach is computationally expensive even for a suboptimal solution. Although several alternative FPCA variants have been developed to improve efficiency, they often shift attention away from equalizing the reconstruction loss – the central goal of FPCA. In this paper, we identify a hidden convexity in FPCA and introduce a new algorithm that solves the resulting convex optimization via an eigenvalue optimization. Our approach achieves the desired fairness in reconstruction loss without sacrificing performance. Experiments on real-world datasets show that the proposed FPCA algorithm is approximately \(8\times \) 8 × faster than the SDR-based algorithm while being at most 85% slower than standard PCA.