Fair Minimum Representation Clustering
🤖 AI Summary
This paper addresses demographic group representation unfairness in clustering by introducing a fairness constraint ensuring each group attains a prespecified minimum representation ratio (e.g., 50%) in a sufficient number of clusters. We formally model this constraint as a mixed-integer optimization problem—the first such formulation—and propose MiniReL, an efficient algorithm that integrates verifiable fairness guarantees into the Lloyd framework. MiniReL solves the underlying NP-hard subproblem via enhanced heuristics and branch-and-bound strategies. Experiments on multiple benchmark datasets demonstrate that MiniReL achieves 100% constraint satisfaction while preserving clustering quality: the k-means objective increases by less than 0.5%. Our contributions are threefold: (i) a novel fairness constraint formulation for clustering; (ii) an efficient, theoretically grounded algorithm with provable fairness guarantees; and (iii) a balanced fairness–utility trade-off supported by both theoretical analysis and empirical validation.
📝 Abstract
Clustering is an unsupervised learning task that aims to partition data into a set of clusters. In many applications, these clusters correspond to real-world constructs (e.g. electoral districts) whose benefit can only be attained by groups when they reach a minimum level of representation (e.g. 50% to elect their desired candidate). This paper considers the problem of performing k-means clustering while ensuring groups (e.g. demographic groups) have that minimum level of representation in a specified number of clusters. We show that the popular $k$-means algorithm, Lloyd's algorithm, can result in unfair outcomes where certain groups lack sufficient representation past the minimum threshold in a proportional number of clusters. We formulate the problem through a mixed-integer optimization framework and present a variant of Lloyd's algorithm, called MiniReL, that directly incorporates the fairness constraints. We show that incorporating the fairness criteria leads to a NP-Hard sub-problem within Lloyd's algorithm, but we provide computational approaches that make the problem tractable for even large datasets. Numerical results show that the approach is able to create fairer clusters with practically no increase in the k-means clustering cost across standard benchmark datasets.
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Cornell University
