Bulletin of Mathematical Biology

, Volume 81, Issue 2, pp 568–597 | Cite as

Tropical Principal Component Analysis and Its Application to Phylogenetics

  • Ruriko YoshidaEmail author
  • Leon Zhang
  • Xu Zhang
Special Issue: Algebraic Methods in Phylogenetics


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.


Dimensionality reduction Phylogenomics Tropical geometry 



R. Y. was supported by Research Initiation Proposals from the Naval Postgraduate School and NSF Division of Mathematical Sciences 1622369. L. Z. was supported by an NSF Graduate Research Fellowship. X. Z. was supported by travel funding from the Department of Statistics at the University of Kentucky. The authors thank Bernd Sturmfels (UC Berkeley and MPI Leipzig) for many helpful conversations. The authors also thank Daniel Howe (University of Kentucky) for his input on Apicomplexa tree topologies.


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© 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.Naval Postgraduate SchoolMontereyUSA
  2. 2.University of California, BerkeleyBerkeleyUSA
  3. 3.University of KentuckyLexingtonUSA

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