Socially Fair Center-Based and Linear Subspace Clustering

Center-based clustering (e.g., k-means, k-medians) and clustering using linear subspaces are the two most popular objectives for partitioning real-world data into smaller clusters. Both these objectives minimize the average cost of clustering over all the points. However, when the points belong to different sensitive demographic groups and the optimal clustering has a significantly different cost per point for different groups, it can cause fairness-related harms (e.g., different quality-of-service). To mitigate these harms, the socially fair clustering objective minimizes the cost of clustering per point for the worst-off group. In this work, we propose a unified framework to solve socially fair center-based and linear subspace clustering and give practical and efficient approximation algorithms for these problems. We perform extensive experiments to show that our algorithms closely match or outperform existing baselines on multiple benchmark datasets.