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Fair principal component analysis via eigenvalue optimization
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AI
DOI：10.1007/s10543-026-01109-9.png)
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Abstract
En 中文
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;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$8\times $$\end{document} faster than the SDR-based algorithm while being at most 85% slower than standard PCA.
Keywords:
Principal component analysis
Fair machine learning
Joint numerical range
Trace minimization
Eigenvalue optimization
Journal
B
IF:
1.7
Papers:
48
Citations:
0
