Fair-Capacitated Clustering

Abstract: Traditionally, clustering algorithms focus on partitioning the data into groups of similar instances. The similarity objective, however, is not sufficient in applications where a fair-representation of the groups in terms of protected attributes like gender or race, is required for each cluster. Moreover, in many applications, to make the clusters useful for the end-user, a balanced cardinality among the clusters is required. Our motivation comes from the education domain where studies indicate that students might learn better in diverse student groups and of course groups of similar cardinality are more practical e.g., for group assignments. To this end, we introduce the fair-capacitated clustering problem that partitions the data into clusters of similar instances while ensuring cluster fairness and balancing cluster cardinalities. We propose a two-step solution to the problem: i) we rely on fairlets to generate minimal sets that satisfy the fair constraint and ii) we propose two approaches, namely hierarchical clustering and partitioning-based clustering, to obtain the fair-capacitated clustering. The hierarchical approach embeds the additional cardinality requirements during the merging step while the partitioning-based one alters the assignment step using a knapsack problem formulation to satisfy the additional requirements. Our experiments on four educational datasets show that our approaches deliver well-balanced clusters in terms of both fairness and cardinality while maintaining a good clustering quality.