# Convex Formulations for Fair Principal Component Analysis

arXiv: https://arxiv.org/abs/1802.03765 · HTML: https://mlsanity.com/paper/1802.03765/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2018.

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

- [Efficient fair PCA for fair representation learning](https://mlsanity.com/paper/2302.13319/) (2023)
- [Fast and Efficient MMD-based Fair PCA via Optimization over Stiefel Manifold](https://mlsanity.com/paper/2109.11196/) (2021)
- [Distributionally Robust Fair Principal Components via Geodesic Descents](https://mlsanity.com/paper/2202.03071/) (2022)
- [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 Oversampling Technique using Heterogeneous Clusters](https://mlsanity.com/paper/2305.13875/) (2023)
- [A Joint Matrix Factorization Analysis of Multilingual Representations](https://mlsanity.com/paper/2310.15513/) (2023)
- [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)
- [Fair Column Subset Selection](https://mlsanity.com/paper/2306.04489/) (2023)
- [Sampling a Near Neighbor in High Dimensions -- Who is the Fairest of Them All?](https://mlsanity.com/paper/2101.10905/) (2021)
- [On Socially Fair Low-Rank Approximation and Column Subset Selection](https://mlsanity.com/paper/2412.06063/) (2024)
- [FiSH: Fair Spatial Hotspots](https://mlsanity.com/paper/2106.06049/) (2021)
- [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)
- [Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness](https://mlsanity.com/paper/2209.01229/) (2022)
- [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)
- [Fair PCA, One Component at a Time](https://mlsanity.com/paper/2503.21563/) (2025)
- [Incorporating Fairness Constraints into Archetypal Analysis](https://mlsanity.com/paper/2507.12021/) (2025)

## Abstract (arXiv)

Though there is a growing body of literature on fairness for supervised learning, the problem of incorporating fairness into unsupervised learning has been less well-studied. This paper studies fairness in the context of principal component analysis (PCA). We first present a definition of fairness for dimensionality reduction, and our definition can be interpreted as saying that a reduction is fair if information about a protected class (e.g., race or gender) cannot be inferred from the dimensionality-reduced data points. Next, we develop convex optimization formulations that can improve the fairness (with respect to our definition) of PCA and kernel PCA. These formulations are semidefinite programs (SDP's), and we demonstrate the effectiveness of our formulations using several datasets. We conclude by showing how our approach can be used to perform a fair (with respect to age) clustering of health data that may be used to set health insurance rates.