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Clustering is a fundamental problem in unsupervised machine learning, andfair variants of it have recently received significant attention due to itssocietal implications. In this work we introduce a novel definition ofindividual fairness for clustering problems. Specifically, in our model, eachpoint $j$ has a set of other points $\mathcal{S}_j$ that it perceives assimilar to itself, and it feels that it is fairly treated if the quality ofservice it receives in the solution is $\alpha$-close (in a multiplicativesense, for a given $\alpha \geq 1$) to that of the points in $\mathcal{S}_j$.We begin our study by answering questions regarding the structure of theproblem, namely for what values of $\alpha$ the problem is well-defined, andwhat the behavior of the \emph{Price of Fairness (PoF)} for it is. For thewell-defined region of $\alpha$, we provide efficient and easily-implementableapproximation algorithms for the $k$-center objective, which in certain casesenjoy bounded-PoF guarantees. We finally complement our analysis by anextensive suite of experiments that validates the effectiveness of ourtheoretical results.

A New Notion of Individually Fair Clustering: $\alpha$-Equitable $k$-Center