# Efficient Fair Principal Component Analysis

arXiv: https://arxiv.org/abs/1911.04931 · HTML: https://mlsanity.com/paper/1911.04931/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2019.

## Built on by (most cited first, 20 of 20)

- [Bias Mitigation for Machine Learning Classifiers: A Comprehensive Survey](https://mlsanity.com/paper/2207.07068/) (2022)
- [On Tilted Losses in Machine Learning: Theory and Applications](https://mlsanity.com/paper/2109.06141/) (2021)
- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Pareto Efficient Fairness in Supervised Learning: From Extraction to Tracing](https://mlsanity.com/paper/2104.01634/) (2021)
- [A novel approach for Fair Principal Component Analysis based on eigendecomposition](https://mlsanity.com/paper/2208.11362/) (2022)
- [Fair CoVariance Neural Networks](https://mlsanity.com/paper/2409.08558/) (2024)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)
- [Fairness-Aware Estimation of Graphical Models](https://mlsanity.com/paper/2408.17396/) (2024)
- [Adaptive Distillation: Aggregating Knowledge from Multiple Paths for Efficient Distillation](https://mlsanity.com/paper/2110.09674/) (2021)
- [Fair Canonical Correlation Analysis](https://mlsanity.com/paper/2309.15809/) (2023)
- [Fair principal component analysis (PCA): minorization-maximization algorithms for Fair PCA, Fair Robust PCA and Fair Sparse PCA](https://mlsanity.com/paper/2305.05963/) (2023)
- [A survey on bias in machine learning research](https://mlsanity.com/paper/2308.11254/) (2023)
- [Towards Fairness and Privacy: A Novel Data Pre-processing Optimization Framework for Non-binary Protected Attributes](https://mlsanity.com/paper/2410.00836/) (2024)
- [When Collaborative Filtering is not Collaborative: Unfairness of PCA for Recommendations](https://mlsanity.com/paper/2310.09687/) (2023)
- [On the KL-Divergence-based Robust Satisficing Model](https://mlsanity.com/paper/2408.09157/) (2024)
- [Worst-case low-rank approximations](https://mlsanity.com/paper/2603.11304/) (2026)
- [PLS-based approach for fair representation learning](https://mlsanity.com/paper/2502.16263/) (2025)
- [Achieving Fair PCA Using Joint Eigenvalue Decomposition](https://mlsanity.com/paper/2502.16933/) (2025)
- [Incorporating Fairness Constraints into Archetypal Analysis](https://mlsanity.com/paper/2507.12021/) (2025)
- [From Measurement to Mitigation: Quantifying and Reducing Identity Leakage in Image Representation Encoders with Linear Subspace Removal](https://mlsanity.com/paper/2604.05296/) (2026)

## Abstract (arXiv)

It has been shown that dimension reduction methods such as PCA may be inherently prone to unfairness and treat data from different sensitive groups such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing dimensionality reduction, using the notion of Pareto optimality, we propose an adaptive first-order algorithm to learn a subspace that preserves fairness, while slightly compromising the reconstruction loss. Theoretically, we provide sufficient conditions that the solution of the proposed algorithm belongs to the Pareto frontier for all sensitive groups; thereby, the optimal trade-off between overall reconstruction loss and fairness constraints is guaranteed. We also provide the convergence analysis of our algorithm and show its efficacy through empirical studies on different datasets, which demonstrates superior performance in comparison with state-of-the-art algorithms. The proposed fairness-aware PCA algorithm can be efficiently generalized to multiple group sensitive features and effectively reduce the unfairness decisions in downstream tasks such as classification.