2017/10/07 by Ruriko Yoshida, Yoshida, Ruriko, Leon Zhang +3
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Biological sciences #FOS: Mathematics #Genetic diversity and population structure #Genomics and Phylogenetic Studies #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1710.02682
openalex publication_date 2017/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.