Next Article in Journal
An Algorithm of Image Encryption Using Logistic and Two-Dimensional Chaotic Economic Maps
Next Article in Special Issue
Non-Equilibrium Liouville and Wigner Equations: Classical Statistical Mechanics and Chemical Reactions for Long Times
Previous Article in Journal
Extracting Interactions between Flying Bat Pairs Using Model-Free Methods
Previous Article in Special Issue
A Brief Review of Generalized Entropies
Article Menu
Issue 1 (January) cover image

Export Article

Open AccessReview
Entropy 2019, 21(1), 43;

Approximation of Densities on Riemannian Manifolds

Ecole Nationale de l’Aviation Civile, Université de Toulouse, 31055 Toulouse, France
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 11 December 2018 / Revised: 30 December 2018 / Accepted: 3 January 2019 / Published: 9 January 2019
(This article belongs to the Special Issue 20th Anniversary of Entropy—Review Papers Collection)
PDF [407 KB, uploaded 24 January 2019]


Finding an approximate probability distribution best representing a sample on a measure space is one of the most basic operations in statistics. Many procedures were designed for that purpose when the underlying space is a finite dimensional Euclidean space. In applications, however, such a simple setting may not be adapted and one has to consider data living on a Riemannian manifold. The lack of unique generalizations of the classical distributions, along with theoretical and numerical obstructions require several options to be considered. The present work surveys some possible extensions of well known families of densities to the Riemannian setting, both for parametric and non-parametric estimation. View Full-Text
Keywords: quantization; directional densities; exponential family; group invariance; Riemannian manifold quantization; directional densities; exponential family; group invariance; Riemannian manifold
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

le Brigant, A.; Puechmorel, S. Approximation of Densities on Riemannian Manifolds. Entropy 2019, 21, 43.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top