Tropical Principal Component Analysis and Its Application to Phylogenetics

被引：24
|
作者：
Yoshida, Ruriko [1 ]
Zhang, Leon [2 ]
Zhang, Xu [3 ]
机构：
[1] Naval Postgrad Sch, 1411 Cunningham Rd, Monterey, CA 93943 USA
[2] Univ Calif Berkeley, 1042 Evans Hall, Berkeley, CA 94720 USA
[3] Univ Kentucky, 725 Rose St,Multidisciplinary Sci Bldg 0082, Lexington, KY 40536 USA
来源：
BULLETIN OF MATHEMATICAL BIOLOGY | 2019年 / 81卷 / 02期
基金：
美国国家科学基金会;
关键词：
Dimensionality reduction; Phylogenomics; Tropical geometry; SPACE;
D O I：
10.1007/s11538-018-0493-4
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
Principal component analysis is a widely used method for the dimensionality reduction of a given data set in a high-dimensional Euclidean space. Here we define and analyze two analogues of principal component analysis in the setting of tropical geometry. In one approach, we study the Stiefel tropical linear space of fixed dimension closest to the data points in the tropical projective torus; in the other approach, we consider the tropical polytope with a fixed number of vertices closest to the data points. We then give approximative algorithms for both approaches and apply them to phylogenetics, testing the methods on simulated phylogenetic data and on an empirical dataset of Apicomplexa genomes.
引用
收藏
页码：568 / 597
页数：30
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