用联合特征值分解让PCA更公平，避免群体差异
Achieving Fair PCA Using Joint Eigenvalue Decomposition
- 引入联合特征值分解，同时处理多矩阵以实现公平降维
- 在多个数据集上优于基线方法，兼顾公平性与表征质量
- 适合关注算法公平性的机器学习研究者和应用开发者
主成分分析（PCA）是广泛使用的降维方法，但在包含人口统计特征的数据上常忽略公平性，导致某些群体受到不公平影响。为此，本文提出结合联合特征值分解（JEVD）的方法，通过同时对多个矩阵进行对角化，实现公平高效的表示。我们证明了JEVD的最优解即为公平的PCA解。将JEVD与PCA融合后，既保持了数据结构的完整性，又确保敏感属性不会造成表示上的偏差。实验表明，该方法在多个数据集上均显著优于现有基线，在公平性和表征质量方面表现更优。
原文摘要 · Abstract (English)
Principal Component Analysis (PCA) is a widely used method for dimensionality reduction, but it often overlooks fairness, especially when working with data that includes demographic characteristics. This can lead to biased representations that disproportionately affect certain groups. To address this issue, our approach incorporates Joint Eigenvalue Decomposition (JEVD), a technique that enables the simultaneous diagonalization of multiple matrices, ensuring fair and efficient representations. We formally show that the optimal solution of JEVD leads to a fair PCA solution. By integrating JEVD with PCA, we strike an optimal balance between preserving data structure and promoting fairness across diverse groups. We demonstrate that our method outperforms existing baseline approaches in fairness and representational quality on various datasets. It retains the core advantages of PCA while ensuring that sensitive demographic attributes do not create disparities in the reduced representation.
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