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Fair k-Means Clustering

Abstract

We show that the popular kk-means clustering algorithm (Lloyd's heuristic), used for a variety of scientific data, can result in outcomes that are unfavorable to subgroups of data (e.g., demographic groups). Such biased clusterings can have deleterious implications for human-centric applications such as resource allocation. We present a fair kk-means objective and algorithm to choose cluster centers that provide equitable costs for different groups. The algorithm, Fair-Lloyd, is a modification of Lloyd's heuristic for kk-means, inheriting its simplicity, efficiency, and stability. In comparison with standard Lloyd's, we find that on benchmark data sets, Fair-Lloyd exhibits unbiased performance by ensuring that all groups have balanced costs in the output kk-clustering, while incurring a negligible increase in running time, thus making it a viable fair option wherever kk-means is currently used.

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