Tropical principal component analysis on the space of ultrametrics

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Yoshida_Tropical_principal_component_analysis_on_the_space_of_ultrametrics.pdf (3.55 MB)
Authors
Page, Robert
Yoshida, Ruriko
Zhang, Leon
Subjects
Phylogenetics
Phylogenomics
Tree Spaces
Unsupervised Learning
Advisors
Date of Issue
2019
Date
2019
Publisher
ArXiv
Language
Abstract
In 2019, Yoshida et al. introduced a notion of tropical principal component analysis (PCA). The output is a tropical polytope with a fixed number of vertices that best fits the data. We here apply tropical PCA to dimension reduction and visualization of data sampled from the space of phylogenetic trees. Our main results are twofold: the existence of a tropical cell decomposition into regions of fixed tree topology and the development of a stochastic optimization method to estimate the tropical PCA using a Markov Chain Monte Carlo (MCMC) approach. This method performs well with simulation studies, and it is applied to three empirical datasets: Apicomplexa and African coelacanth genomes as well as sequences of hemagglutinin for influenza from New York.
Type
Preprint
Description
URI
https://hdl.handle.net/10945/64570
Series/Report No
Department
Operations Research (OR)
Organization
Identifiers
NPS Report Number
Sponsors
National Science Foundation for partially supporting R.Y. (DMS 1916037) and L.Z. (NSF Graduate Research Fellowship)
Funder
National Science Foundation for partially supporting R.Y. (DMS 1916037) and L.Z. (NSF Graduate Research Fellowship)
Format
26 p.
Citation
Page, Robert, Leon Zhang, and Ruriko Yoshida. "Tropical principal component analysis on the space of ultrametrics." arXiv preprint arXiv:1911.10675 (2019).
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.
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