  It has been shown that dimension reduction methods such as PCA may be
inherently prone to unfairness and treat data from different sensitive groups
such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing
dimensionality reduction, using the notion of Pareto optimality, we propose an
adaptive first-order algorithm to learn a subspace that preserves fairness,
while slightly compromising the reconstruction loss. Theoretically, we provide
sufficient conditions that the solution of the proposed algorithm belongs to
the Pareto frontier for all sensitive groups; thereby, the optimal trade-off
between overall reconstruction loss and fairness constraints is guaranteed. We
also provide the convergence analysis of our algorithm and show its efficacy
through empirical studies on different datasets, which demonstrates superior
performance in comparison with state-of-the-art algorithms. The proposed
fairness-aware PCA algorithm can be efficiently generalized to multiple group
sensitive features and effectively reduce the unfairness decisions in
downstream tasks such as classification.
