Functional data analysis (FDA) is a statistical framework that allows for the analysis of
curves, images, or functions on higher dimensional domains. The goals of FDA, such as …

Trees are a canonical structure for representing evolutionary histories. Many popular criteria
used to infer optimal trees are computationally hard, and the number of possible tree shapes …

We consider kernel methods on general geodesic metric spaces and provide both negative
and positive results. First we show that the common Gaussian kernel can only be …

The main objective of this book is to introduce the reader to a new way of analyzing object
data, that primarily takes into account the geometry of the spaces of objects measured on the …

Supplement A: Hessian of the Riemannian squared distance. This supplementary material
describes in more length the notions of Riemannian geometry that are underlying the main …

Statistical analysis for populations of networks is widely applicable, but challenging, as
networks have strongly non-Euclidean behaviour. Graph space is an exhaustive framework …

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 …

This paper investigates the computational geometry relevant to calculations of the Fréchet
mean and variance for probability distributions on the phylogenetic tree space of Billera …

We study the geometry of metrics and convexity structures on the space of phylogenetic
trees, which is here realized as the tropical linear space of all ultrametrics. The CAT(0) …

We propose a new space of phylogenetic trees which we call wald space. The motivation is
to develop a space suitable for statistical analysis of phylogenies, but with a geometry based …