Ruriko Yoshida (Naval Postgraduate School)
Tuesday, January 16, 2018 - 10:00
MPI für Mathematik in den Naturwissenschaften Leipzig
Inselstr. 22, 04103 Leipzig, E1 05 (Leibniz-Saal), 1. Etage
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. This is joint with with Leon Zhang and Xu Zhang.
submitted by Saskia Gutzschebauch (Saskia.Gutzschebauch@mis.mpg.de, 0341 9959 50)