# Analysis of Trade-offs in Fair Principal Component Analysis Based on Multi-objective Optimization

arXiv: https://arxiv.org/abs/2006.06137 · HTML: https://mlsanity.com/paper/2006.06137/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

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

- [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)

## Abstract (arXiv)

In dimensionality reduction problems, the adopted technique may produce disparities between the representation errors of different groups. For instance, in the projected space, a specific class can be better represented in comparison with another one. In some situations, this unfair result may introduce ethical concerns. Aiming at overcoming this inconvenience, a fairness measure can be considered when performing dimensionality reduction through Principal Component Analysis. However, a solution that increases fairness tends to increase the overall re-construction error. In this context, this paper proposes to address this trade-off by means of a multi-objective-based approach. For this purpose, we adopt a fairness measure associated with the disparity between the representation errors of different groups. Moreover, we investigate if the solution of a classical Principal Component Analysis can be used to find a fair projection. Numerical experiments attest that a fairer result can be achieved with a very small loss in the overall reconstruction error.