Proportionally Representative Clustering

In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on clustering -- one of the fundamental tasks in unsupervised machine learning. We propose a new axiom ``proportional representation fairness'' (PRF) that is designed for clustering problems where the selection of centroids reflects the distribution of data points and how tightly they are clustered together. Our fairness concept is not satisfied by existing fair clustering algorithms. We design efficient algorithms to achieve PRF both for unconstrained and discrete clustering problems. Our algorithm for the unconstrained setting is also the first known polynomial-time approximation algorithm for the well-studied Proportional Fairness (PF) axiom (Chen, Fain, Lyu, and Munagala, ICML, 2019). Our algorithm for the discrete setting also matches the best known approximation factor for PF.Comment: Revised version includes a new author (Jeremy Vollen) and new results: Our algorithm for the unconstrained setting is also the first known polynomial-time approximation algorithm for the well-studied Proportional Fairness (PF) axiom (Chen, Fain, Lyu, and Munagala, ICML, 2019). Our algorithm for the discrete setting also matches the best known approximation factor for P