  Principal component analysis (PCA), a ubiquitous dimensionality reduction
technique in signal processing, searches for a projection matrix that minimizes
the mean squared error between the reduced dataset and the original one. Since
classical PCA is not tailored to address concerns related to fairness, its
application to actual problems may lead to disparity in the reconstruction
errors of different groups (e.g., men and women, whites and blacks, etc.), with
potentially harmful consequences such as the introduction of bias towards
sensitive groups. Although several fair versions of PCA have been proposed
recently, there still remains a fundamental gap in the search for algorithms
that are simple enough to be deployed in real systems. To address this, we
propose a novel PCA algorithm which tackles fairness issues by means of a
simple strategy comprising a one-dimensional search which exploits the
closed-form solution of PCA. As attested by numerical experiments, the proposal
can significantly improve fairness with a very small loss in the overall
reconstruction error and without resorting to complex optimization schemes.
Moreover, our findings are consistent in several real situations as well as in
scenarios with both unbalanced and balanced datasets.
