A New Notion of Individually Fair Clustering: α-Equitable k-Center

Clustering is a fundamental problem in unsupervised machine learning, and fair variants of it have recently received significant attention due to its societal implications. In this work we introduce a novel definition of individual fairness for clustering problems. Specifically, in our model, each point j has a set of other points Sj that it perceives as similar to itself, and it feels that it is fairly treated if the quality of service it receives in the solution is α-close (in a multiplicative sense, for a given α ≥ 1) to that of the points in Sj. We begin our study by answering questions regarding the structure of the problem, namely for what values of α the problem is well-defined, and what the behavior of the Price of Fairness (PoF) for it is. For the well-defined region of α, we provide efficient and easily-implementable approximation algorithms for the k-center objective, which in certain cases enjoy bounded-PoF guarantees. We finally complement our analysis by an extensive suite of experiments that validates the effectiveness of our theoretical results.