Achieving Fair PCA Using Joint Eigenvalue Decomposition

TL;DR

This paper introduces a novel fair PCA method using Joint Eigenvalue Decomposition (JEVD) to produce unbiased, equitable data representations across demographic groups, improving fairness without sacrificing data structure.

Contribution

It presents a formal connection between JEVD and fair PCA, offering a new technique that balances data fidelity and fairness in dimensionality reduction.

Findings

Outperforms baseline fairness methods on multiple datasets

Ensures demographic fairness while maintaining data structure

Provides theoretical guarantees for fair PCA solution

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.