Attraction-Repulsion clustering with applications to fairness

In the framework of fair learning, we consider clustering methods that avoid or limit the influence of a set of protected attributes, $S$, (race, sex, etc) over the resulting clusters, with the goal of producing a fair clustering. For this, we introduce perturbations to the Euclidean distance that take into account $S$ in a way that resembles attraction-repulsion in charged particles in Physics and results in dissimilarities with an easy interpretation. Cluster analysis based on these dissimilarities penalizes homogeneity of the clusters in the attributes $S$, and leads to an improvement in fairness. We illustrate the use of our procedures with both synthetic and real data.