A Scalable Algorithm for Individually Fair K-means Clustering

Abstract

We present a scalable algorithm for the individually fair ($p$, $k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$ points $P$ in a metric space, let $\delta (x)$ for $x\in P$ be the radius of the smallest ball around $x$ containing at least $n/k$ points. A clustering is then called individually fair if it has centers within distance $\delta (x)$ of $x$ for each $x\in P$. While good approximation algorithms are known for this problem no efficient practical algorithms with good theoretical guarantees have been presented. We design the first fast local-search algorithm that runs in ~$O(n{k}^2)$ time and obtains a bicriteria $(O(1),6)$ approximation. Then we show empirically that not only is our algorithm much faster than prior work, but it also produces lower-cost solutions.

32 pages, 2 figures, to appear at the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024