# A novel approach for Fair Principal Component Analysis based on eigendecomposition

arXiv: https://arxiv.org/abs/2208.11362 · HTML: https://mlsanity.com/paper/2208.11362/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 24 Aug 2022.

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

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Fairness in Machine Learning](https://mlsanity.com/paper/2012.15816/) (2020)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Empirical observation of negligible fairness-accuracy trade-offs in machine learning for public policy](https://mlsanity.com/paper/2012.02972/) (2020)
- [Fairness in Semi-supervised Learning: Unlabeled Data Help to Reduce Discrimination](https://mlsanity.com/paper/2009.12040/) (2020)
- [Convex Formulations for Fair Principal Component Analysis](https://mlsanity.com/paper/1802.03765/) (2018)
- [Efficient Fair Principal Component Analysis](https://mlsanity.com/paper/1911.04931/) (2019)
- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [Constructing Energy-efficient Mixed-precision Neural Networks through Principal Component Analysis for Edge Intelligence](https://mlsanity.com/paper/1906.01493/) (2019)
- [Fair Principal Component Analysis and Filter Design](https://mlsanity.com/paper/2002.06557/) (2020)
- [Supervised Discriminative Sparse PCA for Com-Characteristic Gene Selection and Tumor Classification on Multiview Biological Data](https://mlsanity.com/paper/1905.11837/) (2019)
- [Multi-Criteria Dimensionality Reduction with Applications to Fairness](https://mlsanity.com/paper/1902.11281/) (2019)

## Built on by (most cited first, 6 of 6)

- [Fair CoVariance Neural Networks](https://mlsanity.com/paper/2409.08558/) (2024)
- [A statistical approach to detect sensitive features in a group fairness setting](https://mlsanity.com/paper/2305.06994/) (2023)
- [When Collaborative Filtering is not Collaborative: Unfairness of PCA for Recommendations](https://mlsanity.com/paper/2310.09687/) (2023)
- [Hidden Convexity of Fair PCA and Fast Solver via Eigenvalue Optimization](https://mlsanity.com/paper/2503.00299/) (2025)
- [Achieving Fair PCA Using Joint Eigenvalue Decomposition](https://mlsanity.com/paper/2502.16933/) (2025)
- [Fair PCA, One Component at a Time](https://mlsanity.com/paper/2503.21563/) (2025)

## Abstract (arXiv)

Principal component analysis (PCA), a ubiquitous dimensionality reduction technique in signal processing, searches for a projection matrix that minimizes the mean squared error between the reduced dataset and the original one. Since classical PCA is not tailored to address concerns related to fairness, its application to actual problems may lead to disparity in the reconstruction errors of different groups (e.g., men and women, whites and blacks, etc.), with potentially harmful consequences such as the introduction of bias towards sensitive groups. Although several fair versions of PCA have been proposed recently, there still remains a fundamental gap in the search for algorithms that are simple enough to be deployed in real systems. To address this, we propose a novel PCA algorithm which tackles fairness issues by means of a simple strategy comprising a one-dimensional search which exploits the closed-form solution of PCA. As attested by numerical experiments, the proposal can significantly improve fairness with a very small loss in the overall reconstruction error and without resorting to complex optimization schemes. Moreover, our findings are consistent in several real situations as well as in scenarios with both unbalanced and balanced datasets.