Fair Polylog-Approximate Low-Cost Hierarchical Clustering
This work addresses fairness in hierarchical clustering, a structured variant of clustering, by providing a practical algorithm that improves upon previous theoretical and polynomial-approximate methods, though it is incremental in advancing the state-of-the-art.
The paper tackles the problem of achieving fair hierarchical clustering with low cost, breaking the polynomial-approximate barrier to propose the first polylogarithmic-approximate algorithm, thus significantly narrowing the gap between fair and vanilla hierarchical clustering approximations.
Research in fair machine learning, and particularly clustering, has been crucial in recent years given the many ethical controversies that modern intelligent systems have posed. Ahmadian et al. [2020] established the study of fairness in \textit{hierarchical} clustering, a stronger, more structured variant of its well-known flat counterpart, though their proposed algorithm that optimizes for Dasgupta's [2016] famous cost function was highly theoretical. Knittel et al. [2023] then proposed the first practical fair approximation for cost, however they were unable to break the polynomial-approximate barrier they posed as a hurdle of interest. We break this barrier, proposing the first truly polylogarithmic-approximate low-cost fair hierarchical clustering, thus greatly bridging the gap between the best fair and vanilla hierarchical clustering approximations.