A novel multi-objective-based approach to analyze trade-offs in Fair Principal Component Analysis

In dimension reduction problems, the adopted technique may produce disparities between the representation errors of two or more different groups. For instance, in the projected space, a specific class can be better represented in comparison with the other ones. Depending on the situation, this unfair result may introduce ethical concerns. Aiming at overcoming this inconvenience, a fairness measure can be considered when performing dimension reduction through Principal Component Analysis. However, a solution that increases fairness tends to increase the reconstruction error. In other words, there is a trade-off between equity and performance. In this context, this paper proposes to address this trade-off in Fair Principal Component Analysis problems 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 reconstruction error.