  Clustering is a foundational problem in machine learning with numerous
applications. As machine learning increases in ubiquity as a backend for
automated systems, concerns about fairness arise. Much of the current
literature on fairness deals with discrimination against protected classes in
supervised learning (group fairness). We define a different notion of fair
clustering wherein the probability that two points (or a community of points)
become separated is bounded by an increasing function of their pairwise
distance (or community diameter). We capture the situation where data points
represent people who gain some benefit from being clustered together.
Unfairness arises when certain points are deterministically separated, either
arbitrarily or by someone who intends to harm them as in the case of
gerrymandering election districts. In response, we formally define two new
types of fairness in the clustering setting, pairwise fairness and community
preservation. To explore the practicality of our fairness goals, we devise an
approach for extending existing $k$-center algorithms to satisfy these fairness
constraints. Analysis of this approach proves that reasonable approximations
can be achieved while maintaining fairness. In experiments, we compare the
effectiveness of our approach to classical $k$-center algorithms/heuristics and
explore the tradeoff between optimal clustering and fairness.
