  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.
