参数化与流式算法用于欧几里得公平 $k$-中心聚类
Parameterized and Streaming Algorithms for Euclidean Fair $k$-Center Clustering
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中文总结 AI 辅助
针对欧几里得公平k-中心聚类问题，提出参数化近似算法（比率2.732）及流式算法（比率4.464），并优化至2.414和3.828，另设计多项式时间流式算法（比率4.732改进至4.42），实验验证聚类精度显著优于现有方法。
中文摘要 AI 辅助
受机器学习中公平性日益重要性的推动，公平 $k$-中心聚类作为一个基础问题引起了广泛的研究关注。在该问题中，数据集被划分为 $m$ 个不相交的组，目标是选择 $k$ 个数据点作为中心，并受限于从每组中选择的中心数量的上界，旨在最小化任何数据点与其分配中心之间的最大距离。鉴于欧几里得空间在机器学习应用中的普遍性，我们首先针对欧几里得公平 $k$-中心问题开发了一种参数化近似算法，其近似比为 $2.732$。通过将该算法作为后处理阶段整合到面向大规模数据的一次遍历流式框架中，我们获得了 $4.464$ 的近似比。这些比率可以分别进一步改进至 $2.414$ 和 $3.828$，但代价是运行时间关于 $k$ 呈指数增长。为确保多项式时间复杂度，我们进一步设计了一种近似比为 $4.732$ 的一次遍历流式算法，该比率可进一步改进至 $4.42$，优于现有最优比率。最后，大量实验表明，我们的方法在聚类精度方面显著优于现有最先进的方法。
英文摘要
Motivated by the growing importance of fairness in machine learning, fair $k$-center clustering has attracted considerable research attention as a fundamental problem. In this problem, a dataset is partitioned into $m$ disjoint groups, and the objective is to select $k$ data points as centers, subject to upper bounds on the number of centers chosen from each group, aiming to minimize the maximum distance between any data point and its assigned center. Focusing on Euclidean spaces, which are ubiquitous in machine learning applications, we first develop a parameterized approximation algorithm for Euclidean fair $k$-center with an approximation ratio of $2.732$. By incorporating this algorithm as a post-processing stage into a one-pass streaming framework for large-scale data, we obtain an approximation ratio of $4.464$. These ratios can be further respectively improved to $2.414$ and $3.828$ with a runtime exponential on $k$. To ensure polynomial-time complexity, we further design a one-pass streaming algorithm with an approximation ratio of $4.732$, which can be further improved to $4.42$, outperforming the state-of-the-art ratio. Finally, extensive experiments show that our methods significantly outperform state-of-the-art approaches in terms of clustering accuracy.
发表机构
- Fuzhou University（福州大学）
- RMIT University（皇家墨尔本理工大学）
机构由 AI 辅助整理，请以论文原文为准。
