  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.

Combinatorics;Populations and Evolution