Title: Guarantees for Spectral Clustering with Fairness Constraints,
Abstract: Given the widespread popularity of spectral clustering (SC) for partitioning
graph data, we study a version of constrained SC in which we try to incorporate
the fairness notion proposed by Chierichetti et al. (2017). According to this
notion, a clustering is fair if every demographic group is approximately
proportionally represented in each cluster. To this end, we develop variants of
both normalized and unnormalized constrained SC and show that they help find
fairer clusterings on both synthetic and real data. We also provide a rigorous
theoretical analysis of our algorithms. While there have been efforts to
incorporate various constraints into the SC framework, theoretically analyzing
them is a challenging problem. We overcome this by proposing a natural variant
of the stochastic block model where h groups have strong inter-group
connectivity, but also exhibit a "natural" clustering structure which is fair.
We prove that our algorithms can recover this fair clustering with high
probability.