A Notion of Individual Fairness for Clustering

A common distinction in fair machine learning, in particular in fair classification, is between group fairness and individual fairness. In the context of clustering, group fairness has been studied extensively in recent years; however, individual fairness for clustering has hardly been explored. In this paper, we propose a natural notion of individual fairness for clustering. Our notion asks that every data point, on average, is closer to the points in its own cluster than to the points in any other cluster. We study several questions related to our proposed notion of individual fairness. On the negative side, we show that deciding whether a given data set allows for such an individually fair clustering in general is NP-hard. On the positive side, for the special case of a data set lying on the real line, we propose an efficient dynamic programming approach to find an individually fair clustering. For general data sets, we investigate heuristics aimed at minimizing the number of individual fairness violations and compare them to standard clustering approaches on real data sets.