# Principal component analysis and the locus of the Fréchet mean in the space of phylogenetic trees

@article{Nye2016PrincipalCA, title={Principal component analysis and the locus of the Fr{\'e}chet mean in the space of phylogenetic trees}, author={Tom M. W. Nye and Xiaoxian Tang and Grady Weyenberg and Ruriko Yoshida}, journal={Biometrika}, year={2016}, volume={104}, pages={901 - 922} }

Summary Evolutionary relationships are represented by phylogenetic trees, and a phylogenetic analysis of gene sequences typically produces a collection of these trees, one for each gene in the analysis. Analysis of samples of trees is difficult due to the multi‐dimensionality of the space of possible trees. In Euclidean spaces, principal component analysis is a popular method of reducing high‐dimensional data to a low‐dimensional representation that preserves much of the sample's structure…

## 30 Citations

### Tropical principal component analysis on the space of phylogenetic trees

- BiologyBioinform.
- 2020

This work develops a stochastic optimization method to estimate tropical PCs over the space of phylogenetic trees using a Markov Chain Monte Carlo (MCMC) approach that performs well with simulation studies, and it is applied to three empirical datasets.

### Foundations of the Wald Space for Phylogenetic Trees

- Mathematics
- 2022

. Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space…

### Tropical Principal Component Analysis and Its Application to Phylogenetics

- BiologyBulletin of Mathematical Biology
- 2018

This work defines and analyzes two analogues of principal component analysis in the setting of tropical geometry and gives approximative algorithms for both approaches and applies them to phylogenetics, testing the methods on simulated phylogenetic data and on an empirical dataset of Apicomplexa genomes.

### Tropical Principal Component Analysis and Its Application to Phylogenetics

- BiologyBulletin of mathematical biology
- 2019

This work defines and analyzes two analogues of principal component analysis in the setting of tropical geometry and gives approximative algorithms for both approaches and applies them to phylogenetics, testing the methods on simulated phylogenetic data and on an empirical dataset of Apicomplexa genomes.

### Information geometry for phylogenetic trees

- MathematicsJournal of mathematical biology
- 2021

A gradient descent algorithm is derived to project from the ambient space of covariance matrices to wald space and it is shown numerically that the two information geometries (discrete and continuous) are very similar.

### Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective

- Biology
- 2018

A novel framework to study sets of phylogenetic trees based on tropical geometry is proposed and studied, which exhibits analytic, geometric, and topological properties that are desirable for theoretical studies in probability and statistics, as well as increased computational efficiency over the current state-of-the-art.

### Confidence Sets for Phylogenetic Trees

- BiologyJournal of the American Statistical Association
- 2018

This manuscript unify recent computational and probabilistic advances to construct tree–valued confidence sets, identifying the best supported most recent ancestor of the Zika virus, and formally testing the hypothesis that a Floridian dentist with AIDS infected two of his patients with HIV.

### Confidence procedures for phylogenetic trees

- Biology
- 2017

The inferential method is a confidence set for the Fréchet mean of a distribution with support on the metric space of phylogenetic trees, and two exploratory methods are proposed for visualizing collections of trees, which rely on similar tools to the confidence set procedure.

### The space of equidistant phylogenetic cactuses

- Mathematics
- 2021

It is shown that equidistant-cactus space is a CAT(0)-metric space which implies, for example, that there are unique geodesic paths between points, and an encoding of ranked, rooted X-trees in terms of partitions of X provides an alternative proof that the space of ultrametric trees on X is CAT( 0).

### Statistics for Data with Geometric Structure

- MathematicsOberwolfach Reports
- 2019

Statistics for data with geometric structure is an active and diverse topic of research. Applications include manifold spaces in directional data or symmetric positive definite matrices and some…

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