On the cost of essentially fair clusterings

By Ioana Orianna Bercea, Martin Groß, Samir Khuller, Aounon Kumar, Clemens Rösner, Daniel R. Schmidt, Melanie Schmidt. 2018

120 citations recorded by the source corpus.

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased. At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation for the fair $k$-center problem and a $O(t)$-approximation for the fair $k$-median problem, where $t$ is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation for fair $k$-center. We extend and improve the known results. Firstly, we give a 5-approximation for the fair $k$-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximations for all of the classical clustering objectives $k$-center, $k$-supplier, $k$-median, $k$-means and facility location. The latter approximations are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where the centers are already fixed.

Subfields: Artificial Intelligence, Computer Science Applications, Organizational Behavior and Human Resource Management

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Citations in the corpus

Scalable Fair Clustering (2019, background): “In particular, (Rösner & Schmidt, 2018) and (Bercea et al., 2018) studied the fair variant of k-center clustering (as opposed to k-median in our case).”
Fairness in Machine Learning: A Survey (2020, unknown): “[ 23 4]”
Rényi Fair Inference (2019, methodology): “Many recent works on fair clustering propose a two-phase algorithm for solving the K-centers and K-median fair clustering problems [13, 5, 43, 7].”