  Center-based clustering (e.g., $k$-means, $k$-medians) and clustering using
linear subspaces are two most popular techniques to partition real-world data
into smaller clusters. However, when the data consists of sensitive demographic
groups, significantly different clustering cost per point for different
sensitive groups can lead to fairness-related harms (e.g., different
quality-of-service). The goal of socially fair clustering is to minimize the
maximum cost of clustering per point over all groups. In this work, we propose
a unified framework to solve socially fair center-based clustering and linear
subspace clustering, and give practical, efficient approximation algorithms for
these problems. We do extensive experiments to show that on multiple benchmark
datasets our algorithms either closely match or outperform state-of-the-art
baselines.
