  Fair clustering is the process of grouping similar entities together, while
satisfying a mathematically well-defined fairness metric as a constraint. Due
to the practical challenges in precise model specification, the prescribed
fairness constraints are often incomplete and act as proxies to the intended
fairness requirement, leading to biased outcomes when the system is deployed.
We examine how to identify the intended fairness constraint for a problem based
on limited demonstrations from an expert. Each demonstration is a clustering
over a subset of the data.
  We present an algorithm to identify the fairness metric from demonstrations
and generate clusters using existing off-the-shelf clustering techniques, and
analyze its theoretical properties. To extend our approach to novel fairness
metrics for which clustering algorithms do not currently exist, we present a
greedy method for clustering. Additionally, we investigate how to generate
interpretable solutions using our approach. Empirical evaluation on three
real-world datasets demonstrates the effectiveness of our approach in quickly
identifying the underlying fairness and interpretability constraints, which are
then used to generate fair and interpretable clusters.
