Wasserstein distances are metrics on probability distributions inspired by the problem of
optimal mass transportation. Roughly speaking, they measure the minimal effort required to …

Mainstream statistical methodology is generally applicable to data observed in Euclidean
space. There are, however, numerous contexts of considerable scientific interest in which …

Hyperbolic embeddings offer excellent quality with few dimensions when embedding
hierarchical data structures. We give a combinatorial construction that embeds trees into …

The quality of the representations achieved by embeddings is determined by how well the
geometry of the embedding space matches the structure of the data. Euclidean space has …

A thoroughly revised and updated edition of this introduction to modern statistical methods
for shape analysis Shape analysis is an important tool in the many disciplines where objects …

Representing images and videos with Symmetric Positive Definite (SPD) matrices, and
considering the Riemannian geometry of the resulting space, has been shown to yield high …

This paper develops the theory of geodesic regression and least-squares estimation on
Riemannian manifolds. Geodesic regression is a method for finding the relationship …

Object oriented data analysis is the statistical analysis of populations of complex objects. In
the special case of functional data analysis, these data objects are curves, where a variety of …

As data is a predominant resource in applications, Riemannian geometry is a natural
framework to model and unify complex nonlinear sources of data. However, the …

Frechet means and Procrustes analysis in Wasserstein space Page 1 Bernoulli 25(2), 2019,
932–976 https://doi.org/10.3150/17-BEJ1009 Fréchet means and Procrustes analysis in …