Clustering without Over-Representation
This addresses fairness and diversity in clustering for applications such as news aggregation, though it appears incremental as it builds on existing clustering frameworks with added constraints.
The paper tackles clustering with color constraints to prevent any color from dominating a cluster, motivated by applications like clustering news articles by source. It presents algorithms with provable guarantees, including a linear programming approach for the general case and a combinatorial method for a special case, showing effectiveness on real-world data.
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.