Deep Fair Discriminative Clustering

Abstract: Deep clustering has the potential to learn a strong representation and hence better clustering performance compared to traditional clustering methods such as $k$-means and spectral clustering. However, this strong representation learning ability may make the clustering unfair by discovering surrogates for protected information which we empirically show in our experiments. In this work, we study a general notion of group-level fairness for both binary and multi-state protected status variables (PSVs). We begin by formulating the group-level fairness problem as an integer linear programming formulation whose totally unimodular constraint matrix means it can be efficiently solved via linear programming. We then show how to inject this solver into a discriminative deep clustering backbone and hence propose a refinement learning algorithm to combine the clustering goal with the fairness objective to learn fair clusters adaptively. Experimental results on real-world datasets demonstrate that our model consistently outperforms state-of-the-art fair clustering algorithms. Our framework shows promising results for novel clustering tasks including flexible fairness constraints, multi-state PSVs and predictive clustering.