  Incorporating fairness constructs into machine learning algorithms is a topic
of much societal importance and recent interest. Clustering, a fundamental task
in unsupervised learning that manifests across a number of web data scenarios,
has also been subject of attention within fair ML research. In this paper, we
develop a novel notion of fairness in clustering, called representativity
fairness. Representativity fairness is motivated by the need to alleviate
disparity across objects' proximity to their assigned cluster representatives,
to aid fairer decision making. We illustrate the importance of representativity
fairness in real-world decision making scenarios involving clustering and
provide ways of quantifying objects' representativity and fairness over it. We
develop a new clustering formulation, RFKM, that targets to optimize for
representativity fairness along with clustering quality. Inspired by the
$K$-Means framework, RFKM incorporates novel loss terms to formulate an
objective function. The RFKM objective and optimization approach guides it
towards clustering configurations that yield higher representativity fairness.
Through an empirical evaluation over a variety of public datasets, we establish
the effectiveness of our method. We illustrate that we are able to
significantly improve representativity fairness at only marginal impact to
clustering quality.
