Tropical principal component analysis and its application to phylogenetics

DOI10.1007/s11538-018-0493-4zbMath1410.92082arXiv1710.02682OpenAlexW2964310952WikidataQ91396484 ScholiaQ91396484MaRDI QIDQ1736948

Xu Zhang, Ruriko Yoshida, Leon Zhang

Publication date: 26 March 2019

Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.02682

zbMATH Keywords

dimensionality reductiontropical geometryphylogenomics

Mathematics Subject Classification ID

Problems related to evolution (92D15) Tropical geometry (14T99)

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Uses Software

• Mesquite

Cites Work

• Unnamed Item
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• Stiefel tropical linear spaces
• Best approximation in max-plus semimodules
• Duality and separation theorems in idempotent semimodules.
• Geometry of the space of phylogenetic trees
• A tropical isoperimetric inequality
• Tropical convexity
• Environmental Kuznets curves: a spatial econometric approach
• Integer Programming with a Fixed Number of Variables
• Assignment Problems
• Max-linear Systems: Theory and Algorithms
• Tropical Fermat--Weber Points
• Essentials of Tropical Combinatorics
• Convexity in Tree Spaces
• Principal component analysis and the locus of the Fréchet mean in the space of phylogenetic trees
• Affine Buildings and Tropical Convexity