Fair Coresets and Streaming Algorithms for Fair k-Means Clustering

Abstract: We study fair clustering problems as proposed by Chierichetti et al. (NIPS 2017). Here, points have a sensitive attribute and all clusters in the solution are required to be balanced with respect to it (to counteract any form of data-inherent bias). Previous algorithms for fair clustering do not scale well. We show how to model and compute so-called coresets for fair clustering problems, which can be used to significantly reduce the input data size. We prove that the coresets are composable and show how to compute them in a streaming setting. Furthermore, we propose a variant of Lloyd's algorithm that computes fair clusterings and extend it to a fair k-means++ clustering algorithm. We implement these algorithms and provide empirical evidence that the combination of our approximation algorithms and the coreset construction yields a scalable algorithm for fair k-means clustering.