Individual Fairness for k-Clustering

Sepideh Mahabadi, Ali Vakilian
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:6586-6596, 2020.

Abstract

We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$. In this work, we show how to get an approximately optimal such fair $k$-clustering: The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor).

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-mahabadi20a, title = {Individual Fairness for k-Clustering}, author = {Mahabadi, Sepideh and Vakilian, Ali}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {6586--6596}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/mahabadi20a/mahabadi20a.pdf}, url = {https://proceedings.mlr.press/v119/mahabadi20a.html}, abstract = {We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$. In this work, we show how to get an approximately optimal such fair $k$-clustering: The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor).} }
Endnote
%0 Conference Paper %T Individual Fairness for k-Clustering %A Sepideh Mahabadi %A Ali Vakilian %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-mahabadi20a %I PMLR %P 6586--6596 %U https://proceedings.mlr.press/v119/mahabadi20a.html %V 119 %X We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$. In this work, we show how to get an approximately optimal such fair $k$-clustering: The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor).
APA
Mahabadi, S. & Vakilian, A.. (2020). Individual Fairness for k-Clustering. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:6586-6596 Available from https://proceedings.mlr.press/v119/mahabadi20a.html.

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