2019/06/20 by Lingxiao Huang, Huang, Lingxiao, Shaofeng H.-C. Jiang +4 · 24 citations
Computer Science · Mathematics · #Advanced Clustering Algorithms Research #Artificial intelligence #Business #Cluster analysis #Computational Geometry (cs.CG) #Computer science #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Data Classification #cs.CG #cs.DS #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.1906.08484
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/06/20 · arxiv created 2019/12/17 · arxiv updated 2019/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent work, [19] studied the following "fair" variants of classical clustering problems such as k-means and k-median: given a set of n data points in ℝd and a binary type associated to each data point, the goal is to cluster the points while ensuring that the proportion of each type in each cluster is roughly the same as its underlying proportion. Subsequent work has focused on either extending this setting to when each data point has multiple, non-disjoint sensitive types such as race and gender [6], or to address the problem that the clustering algorithms in the above work do not scale well. The main contribution of this paper is an approach to clustering with fairness constraints that involve multiple, non-disjoint types, that is also scalable. Our approach is based on novel constructions of coresets: for the k-median objective, we construct an ε-coreset of size O(Γk2 ε-d) where Γ is the number of distinct collections of groups that a point may belong to, and for the k-means objective, we show how to construct an ε-coreset of size O(Γk3ε-d-1). The former result is the first known coreset construction for the fair clustering problem with the k-median objective, and the latter result removes the dependence on the size of the full dataset as in [39] and generalizes it to multiple, non-disjoint types. Plugging our coresets into existing algorithms for fair clustering such as [5] results in the fastest algorithms for several cases. Empirically, we assess our approach over the Adult, Bank, Diabetes and Athlete dataset, and show that the coreset sizes are much smaller than the full dataset. We also achieve a speed-up to recent fair clustering algorithms [5,6] by incorporating our coreset construction.