TROPICAL FERMAT-WEBER POINTS
TROPICAL FERMAT-WEBER POINTS
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DOI：
10.1137/16m1071122
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发表时间：
2018-01-01
影响因子：
0.8
通讯作者：
Yoshida, Ruriko
中科院分区：
文献类型：
--
作者：
Lin, Bo;Yoshida, Ruriko
在度量空间中，样本的Fermat-Weber点是度量样本集中趋势的统计量，并且众所周知，样本的Fermat-Weber点在度量空间中不一定是唯一的。研究了商空间R-n/R1（n是N的元素）上热带度量下Fermat-Weber点的计算，其动机是将其应用于具有N个叶的等距系统发生树空间（在这种情况下n =（（N）（2））），该空间实现为所有超度量的热带线性空间.我们证明了有限样本的所有热带Fermat-Weber点的集合总是一个经典的凸多面体，并给出了与此集合相关的一个键值的组合公式。我们确定的条件下，这套是一个单例。我们应用数值实验来分析一组热带Fermat-Weber点的系统发育树的空间内。讨论了热带Fermat-Weber点的计算问题。
In a metric space, the Fermat-Weber points of a sample are statistics to measure the central tendency of the sample and it is well known that the Fermat-Weber point of a sample is not necessarily unique in the metric space. We investigate the computation of Fermat-Weber points under the tropical metric on the quotient space R-n/R1 with a fixed n is an element of N, motivated by its application to the space of equidistant phylogenetic trees with N leaves (in this case n = ((N)(2))) realized as the tropical linear space of all ultrametrics. We show that the set of all tropical Fermat-Weber points of a finite sample is always a classical convex polytope, and we present a combinatorial formula for a key value associated with this set. We identify conditions under which this set is a singleton. We apply numerical experiments to analyze the set of the tropical Fermat-Weber points within a space of phylogenetic trees. We discuss the issues in the computation of the tropical Fermat-Weber points.