Given the widespread popularity of spectral clustering (SC) for partitioning graph data, we study a version of constrained SC in which we try to incorporate the fairness notion proposed by Chierichetti et al. (2017). According to this notion, a clustering is fair if every demographic group is approximately proportionally represented in each cluster. To this end, we develop variants of both normalized and unnormalized constrained SC and show that they help find fairer clusterings on both synthetic and real data. We also provide a rigorous theoretical analysis of our algorithms. While there have been efforts to incorporate various constraints into the SC framework, theoretically analyzing them is a challenging problem. We overcome this by proposing a natural variant of the stochastic block model where h groups have strong inter-group connectivity, but also exhibit a "natural" clustering structure which is fair. We prove that our algorithms can recover this fair clustering with high probability.

本研究研究了一种受Chierichetti等人提出的公平原则约束的、用于对图形数据进行分区的谱聚类方法。我们开发了归一化和非归一化受约束谱聚类的变体，并证明它们可以在合成和真实数据上找到更公平的聚类结构。在一种自然环境变体的随机块模型上，我们对算法进行了严格的理论分析，并证明我们的算法可以以高概率恢复这种公平聚类。

具有公平约束的谱聚类的保证