Local Search-based Individually Fair Clustering with Outliers

2025-10-07

AI Summary

This paper studies individually fair clustering under the presence of outliers—ensuring that each inlier point has at least one cluster center within its $n/k$-nearest neighbors (individual fairness) while robustly mitigating outlier influence. To this end, we propose the first local search framework that jointly incorporates outlier removal and individual fairness constraints. We design a scalable randomized local search algorithm that iteratively optimizes both cluster center selection and outlier identification. We provide rigorous theoretical guarantees on both the approximation ratio and the number of outliers removed. Experiments on multiple real-world datasets demonstrate that our method significantly improves clustering quality and fairness guarantees for inliers, while maintaining high efficiency and scalability—making it suitable for large-scale practical applications.

Technology Category

• Machine Learning: Clustering
• Search and Optimization: Local Search
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

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.

Problem

• Developing scalable fair clustering with outlier removal using local search
• Addressing suboptimal fairness caused by outliers in clustering algorithms
• Providing approximation guarantees while bounding discarded outlier count

Innovation

• Local search algorithm for fair clustering with outliers
• Discards outliers to compute fair centers
• Randomized local search ensures scalability to large datasets