离散Fréchet和Hausdorff距离下的k-中值聚类
k-Median clustering under discrete Fréchet and Hausdorff distances
摘要：
给出了离散Fréchet距离下多边形轨迹的$k$中值聚类的第一个近似线性时间$(1+\eps)$近似算法，以及Hausdorff距离下有限点集的$k$中值聚类的第一个多项式时间$(1+\eps)$近似算法，条件是聚类中心、环境维数和$k$都有一个常数的界.主要的技术是一个通用的框架来解决聚类问题的聚类中心被限制来自一个\emph{simpler}度量空间。我们精确地描述了条件上的更简单的度量空间的集群中心，允许更快的$(1+\eps)$ -近似的$k$ -中位数问题。我们还证明了Hausdorff距离下的$k$ -中值问题是\textsc{NP-Hard} .
英文摘要：
We give the first near-linear time $(1+\eps)$-approximation algorithm for $k$-median clustering of polygonal trajectories under the discrete Fréchet distance, and the first polynomial time $(1+\eps)$-approximation algorithm for $k$-median clustering of finite point sets under the Hausdorff distance, provided the cluster centers, ambient dimension, and $k$ are bounded by a constant. The main technique is a general framework for solving clustering problems where the cluster centers are restricted to come from a \emph{simpler} metric space. We precisely characterize conditions on the simpler metric space of the cluster centers that allow faster $(1+\eps)$-approximations for the $k$-median problem. We also show that the $k$-median problem under Hausdorff distance is \textsc{NP-Hard}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
