  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.
