Related papers: Warped Riemannian metrics for location-scale model…

In Theorem 1, we generalize the results of Szabo for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F. As an application we show…

We show that compact Riemannian manifolds, regarded as metric spaces with their global geodesic distance, cannot contain a number of rigid structures such as (a) arbitrarily large regular simplices or (b) arbitrarily long sequences of…

We introduce dynamic and static formulations that formally extend unbalanced optimal transport from the space of positive densities to the space of Riemannian metrics. The first construction is based on a dynamic variational formulation in…

The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. This paper develops practical applications of spread dimension in the context of machine…

We study Cartan-Schouten metrics, explore invariant dual connections, and propose them as models for Information Geometry. Based on the underlying Riemannian barycenter and the biinvariant mean of Lie groups, we subsequently propose a new…

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic subspaces of a fixed dimension. It features in a large variety of applications in physics and engineering. In this work, we study this manifold with the…

Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian…

The Fisher's information metric is introduced in order to find the real meaning of the probability distribution in classical and quantum systems described by Riemaniann non-degenerated superspaces. In particular, the physical r\^{o}le…

Mahalanobis distance is a classical tool in multivariate analysis. We suggest here an extension of this concept to the case of functional data. More precisely, the proposed definition concerns those statistical problems where the sample…

In this paper we introduce a new approach to variational problems on the space Riem(M^n) of Riemannian structures (i.e. isometry classes of Riemannan metrics) on any fixed compact manifold M^n of dimension n >= 5. This approach often…

Riemannian metrics on the position-orientation space M(3) that are roto-translation group SE(3) invariant play a key role in image analysis tasks like enhancement, denoising, and segmentation. These metrics enable roto-translation…

Data sets tend to live in low-dimensional non-linear subspaces. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The symmetric Riemannian geometry setting can be suitable for a variety of…

A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new even for isometries of Banach spaces as well as for non-locally compact…

In a previous paper the authors developed a H^1-BMO theory for unbounded metric measure spaces $(M,\rho,m)$ of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and…

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…

Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…

We introduce a novel geometric framework for separating the phase and the amplitude variability in functional data of the type frequently studied in growth curve analysis. This framework uses the Fisher-Rao Riemannian metric to derive a…

On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip this set with an extended metric which is connected if and…

This paper makes some modifications to the warped product space. Based on Alias,Impera and Rigoli, a warping function is added to the warped product space. This new function affects the Riemannian metric of the warped product space. In this…

We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices. The estimator is positive definite by construction, and the…