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arXiv · 2510.06130

Local Search-based Individually Fair Clustering with Outliers

Binita Maity·Shrutimoy Das·Anirban Dasgupta
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Abstract

In this paper, we present a local search-based algorithm for individually fair clustering in the presence of outliers. We consider the individual fairness definition proposed in Jung et al., which requires that each of the $n$ points in the dataset must have one of the $k$ centers within its $n/k$ nearest neighbors. However, if the dataset is known to contain outliers, the set of fair centers obtained under this definition might be suboptimal for non-outlier points. In order to address this issue, we propose a method that discards a set of points marked as outliers and computes the set of fair centers for the remaining non-outlier points. Our method utilizes a randomized variant of local search, which makes it scalable to large datasets. We also provide an approximation guarantee of our method as well as a bound on the number of outliers discarded. Additionally, we demonstrate our claims experimentally on a set of real-world datasets.

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Binita Maity, Shrutimoy Das, Anirban Dasgupta. 2025-10-07. Local Search-based Individually Fair Clustering with Outliers. https://arxiv.org/abs/2510.06130

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