  There has been much interest recently in developing fair clustering
algorithms that seek to do justice to the representation of groups defined
along sensitive attributes such as race and gender. We observe that clustering
algorithms could generate clusters such that different groups are disadvantaged
within different clusters. We develop a clustering algorithm, building upon the
centroid clustering paradigm pioneered by classical algorithms such as
$k$-means, where we focus on mitigating the unfairness experienced by the
most-disadvantaged group within each cluster. Our method uses an iterative
optimisation paradigm whereby an initial cluster assignment is modified by
reassigning objects to clusters such that the worst-off sensitive group within
each cluster is benefitted. We demonstrate the effectiveness of our method
through extensive empirical evaluations over a novel evaluation metric on
real-world datasets. Specifically, we show that our method is effective in
enhancing cluster-level group representativity fairness significantly at low
impact on cluster coherence.
