Fair k-Center Clustering for Data Summarization

Abstract

In data summarization we want to choose $k$ prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose $k_i$ prototypes belonging to group $i$. A common approach to the problem without the fairness constraint is to optimize a centroid-based clustering objective such as $k$-center. A natural extension then is to incorporate the fairness constraint into the clustering problem. Existing algorithms for doing so run in time super-quadratic in the size of the data set, which is in contrast to the standard $k$-center problem being approximable in linear time. In this paper, we resolve this gap by providing a simple approximation algorithm for the $k$-center problem under the fairness constraint with running time linear in the size of the data set and $k$. If the number of demographic groups is small, the approximation guarantee of our algorithm only incurs a constant-factor overhead.

References in corpus (4)

• Equality of Opportunity in Supervised Learning
• Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings
• Guarantees for Spectral Clustering with Fairness Constraints
• Fair Coresets and Streaming Algorithms for Fair k-Means Clustering

Cited by in corpus (9)

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• Representativity Fairness in Clustering
• Streaming Algorithms for Diversity Maximization with Fairness Constraints
• Diverse Data Selection under Fairness Constraints
• Fairness-aware Model-agnostic Positive and Unlabeled Learning
• Faster Algorithms for Fair Max-Min Diversification in ${\mathbb{R}}^d$
• Spectral Normalized-Cut Graph Partitioning with Fairness Constraints
• Max-Min Diversification with Fairness Constraints: Exact and Approximation Algorithms
• Fair Set Cover