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 ~$O(nk^2)$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.06730
- arXiv:
- arXiv:2402.06730
- Bibcode:
- 2024arXiv240206730B
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- Computer Science - Computers and Society;
- Computer Science - Machine Learning
- E-Print:
- 32 pages, 2 figures, to appear at the 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024