Proportionally Representative Clustering

• URL: http://arxiv.org/abs/2304.13917v3
• Date: Mon, 04 Nov 2024 04:08:09 GMT
• Title: Proportionally Representative Clustering
• Authors: Haris Aziz, Barton E. Lee, Sean Morota Chu, Jeremy Vollen,
• Abstract summary: We propose a new axiom proportionally representative fairness'' (PRF) that is designed for clustering problems. Our fairness concept is not satisfied by existing fair clustering algorithms. Our algorithm for the unconstrained setting is also the first known-time approximation algorithm for the well-studied Proportional Fairness (PF) axiom.
• Score: 17.5359577544947
• License:
• Abstract: In recent years, there has been a surge in effort to formalize notions of fairness in machine learning. We focus on centroid clustering--one of the fundamental tasks in unsupervised machine learning. We propose a new axiom ``proportionally representative 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. Our algorithm for the discrete setting also matches the best known approximation factor for PF.

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