Clustering without Over-Representation

Abstract

In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in any cluster. This problem is motivated by practical clustering settings, e.g., in clustering news articles where the color of an article is its source, it is preferable that no single news source dominates any cluster.For the most general version of this problem, we obtain an algorithm that has provable guarantees of performance; our algorithm is based on finding a fractional solution using a linear program and rounding the solution subsequently. For the special case of the problem where no color has an absolute majority in any cluster, we obtain a simpler combinatorial algorithm also with provable guarantees. Experiments on real-world data shows that our algorithms are effective in finding good clustering without over-representation. CCS CONCEPTS• Information systems → Clustering; Data mining; • Theory of computation → Facility location and clustering; Unsupervised learning and clustering. ACM Reference Format:

An Overview of Fairness in Clustering

“…Other group-level fairness notions include bounded representation [86] which considers two parameters α and β which denote the allowed maximum and minimum pro-portions of protected group members that can be present in a cluster. Thus, through this notion no protected group members should be over or under preferred for each cluster.…”

“…The notion of bounded representation was proposed by Ahmadian et al [86]. It is a group-level notion and can be defined using two parameters α and β.…”

“…If α = β = 1/m then the notion aims to represent each group with equal proportion in the clustering output. Bounded representation has been used in conjunction with a number of clustering objectives as well [86], [105].…”

“…Content may change prior to final publication. [97], [98], [99], [100], [112], [105], [32], [113], [111], [114], [115], [116], [102], [117], [101] Bounded Representation clustering algorithm is constrained by two parameters that define the allowed maximum and minimum proportions of protected group members in a cluster any [86] [105], [85], [86], [97], [118], [119], [ remove the dependence of dimension for fair coreset generation in the case of k-means. Further, their approach works for multiple disjoint protected groups.…”

“…A number of papers expanded upon the original fairness notion of balance [30] by introducing upper and/or lower bounds to protected group membership in clusters, also previously referred to as the bounded representation notion. Ahmadian et al [86] used only an upper bound constraint for protected group representation in clusters for fair kcenter with multiple protected groups present. Bera et al [85] and Bercea at al [98] provided approaches for more general clustering objectives that used upper and lower bound constraints on the proportion of protected group members in each cluster.…”