# Hidden Convexity of Fair PCA and Fast Solver via Eigenvalue Optimization

arXiv: https://arxiv.org/abs/2503.00299 · HTML: https://mlsanity.com/paper/2503.00299/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 1 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [Fair Algorithms for Clustering](https://mlsanity.com/paper/1901.02393/) (2019)
- [Face Image Quality Assessment: A Literature Survey](https://mlsanity.com/paper/2009.01103/) (2020)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Masked Face Recognition Dataset and Application](https://mlsanity.com/paper/2003.09093/) (2020)
- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Convex Formulations for Fair Principal Component Analysis](https://mlsanity.com/paper/1802.03765/) (2018)
- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [A novel approach for Fair Principal Component Analysis based on eigendecomposition](https://mlsanity.com/paper/2208.11362/) (2022)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)

## Built on by (most cited first, 1 of 1)

- [Fair PCA, One Component at a Time](https://mlsanity.com/paper/2503.21563/) (2025)

## Abstract (arXiv)

Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying datasets. To address the bias issue, a Fair PCA (FPCA) model was introduced by Samadi et al. (2018) for equalizing the reconstruction loss between subgroups. The semidefinite relaxation (SDR) based approach proposed by Samadi et al. (2018) is computationally expensive even for suboptimal solutions. To improve efficiency, several alternative variants of the FPCA model have been developed. These variants often shift the focus away from equalizing the reconstruction loss. In this paper, we identify a hidden convexity in the FPCA model and introduce an algorithm for convex optimization via eigenvalue optimization. Our approach achieves the desired fairness in reconstruction loss without sacrificing performance. As demonstrated in real-world datasets, the proposed FPCA algorithm runs 8× faster than the SDR-based algorithm, and only at most 85% slower than the standard PCA.