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Estimating Tropical Principal Components Using Metropolis Hasting Algorithm

  • Qiwen Kang
  • Ruriko YoshidaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

Principal component analysis is one of the most popular unsupervised learning methods for reducing the dimension of a given data set in a high-dimensional Euclidean space. However, computing principal components on a space of phylogenetic trees with fixed labels of leaves is a challenging task since a space of phylogenetic tree is not Euclidean. In 2017, Yoshida et al. defined a notion of tropical principal component analysis and they have applied it to a space of phylogenetic trees. The challenge, however, they encountered was a computational times.

In this paper we estimate tropical principal components in a space of phylogenetic trees using the Metropolis-Hasting algorithm. We have implemented an R software package to efficiently estimate tropical principal components and then we have applied it to African coelacanth genomes data set.

Keywords

Phylogenetic trees Polytopes Tropical geometry 

Notes

Acknowledgements

R. Y. is supported by NSF Division of Mathematical Sciences: CDS&E-MSS program. Proposal number:1622369.

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Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2018

Authors and Affiliations

  1. 1.University of KentuckyLexingtonUSA
  2. 2.Naval Postgraduate SchoolMontereyUSA

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