Efficient algorithms for fair clustering with a new notion of fairness

We revisit the problem of fair clustering, first introduced by Chierichetti et al., that requires each protected attribute to have approximately equal representation in every cluster; i.e., a balance property. Existing solutions clustering are either not scalable or do achieve an optimal trade-off between objective and fairness. In this paper, we propose new notion fairness, which call $tau$-fair strictly generalizes property enables fine-grained efficiency vs. fairness trade-off. Furthermore, show simple greedy round-robin based algorithms efficiently. Under more general setting multi-valued attributes, rigorously analyze theoretical properties our algorithms. Our experimental results suggest proposed solution outperforms all state-of-the-art works exceptionally well even for large number clusters.