Tropical principal component analysis and its application to phylogenetics
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Authors
Yoshida, Ruriko
Zhang, Leon
Zhang, Xu
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Date of Issue
2017-10-15
Date
2017-1-
Publisher
ArXiv
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Abstract
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 dimen- sion 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
Type
Preprint
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Department
Operations Research (OR)
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Format
28 p.
Citation
Yoshida, Ruriko, Leon Zhang, and Xu Zhang. "Tropical Principal Component Analysis and its Application to Phylogenetics." arXiv preprint arXiv:1710.02682 (2017).
Distribution Statement
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.