# Fair principal component analysis (PCA): minorization-maximization algorithms for Fair PCA, Fair Robust PCA and Fair Sparse PCA

arXiv: https://arxiv.org/abs/2305.05963 · HTML: https://mlsanity.com/paper/2305.05963/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 10 May 2023.

## Builds on (most cited first, 5 of 5)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [The Price of Fair PCA: One Extra Dimension](https://mlsanity.com/paper/1811.00103/) (2018)
- [Efficient Fair Principal Component Analysis](https://mlsanity.com/paper/1911.04931/) (2019)
- [Fair Principal Component Analysis and Filter Design](https://mlsanity.com/paper/2002.06557/) (2020)
- [Max-Min Fairness Design for MIMO Interference Channels: a Minorization-Maximization Approach](https://mlsanity.com/paper/1908.00160/) (2019)

## Built on by (most cited first, 2 of 2)

- [Worst-case low-rank approximations](https://mlsanity.com/paper/2603.11304/) (2026)
- [Fair PCA, One Component at a Time](https://mlsanity.com/paper/2503.21563/) (2025)

## Abstract (arXiv)

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the minorization-maximization (MM) approach. The proposed algorithm relies on the relaxation of a semi-orthogonality constraint which is proved to be tight at every iteration of the algorithm. The vanilla version of the proposed algorithm requires solving a semi-definite program (SDP) at every iteration, which can be further simplified to a quadratic program by formulating the dual of the surrogate maximization problem. We also propose two important reformulations of the fair PCA problem: a) fair robust PCA -- which can handle outliers in the data, and b) fair sparse PCA -- which can enforce sparsity on the estimated fair principal components. The proposed algorithms are computationally efficient and monotonically increase their respective design objectives at every iteration. An added feature of the proposed algorithms is that they do not require the selection of any hyperparameter (except for the fair sparse PCA case where a penalty parameter that controls the sparsity has to be chosen by the user). We numerically compare the performance of the proposed methods with two of the state-of-the-art approaches on synthetic data sets and a real-life data set.