Achieving Fair PCA Using Joint Eigenvalue Decomposition
Vidhi Rathore, Naresh Manwani
TL;DR
$PCA$ often yields biased reduced representations when sensitive attributes are present. The paper proposes a JEVD-based Fair PCA that jointly diagonalizes two group-specific matrices to enforce fairness while preserving data structure. Key contributions include a simplified reconstruction-loss formulation, a theoretical link showing JEVD minimization yields fair PCA, a fast $O(d^3)$ JEVD-PCA algorithm, and empirical validation on four datasets showing improved fairness (lower $MMD^2$) with competitive reconstruction quality. The approach offers a scalable and practical mechanism for fair dimensionality reduction in domains where demographic attributes must not distort representations.
Abstract
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.