Kernel Density Estimation on Spaces of Gaussian Distributions and Symmetric Positive Definite Matrices

DOI10.1137/15M1053566zbMath1422.62136OpenAlexW2587279402MaRDI QIDQ5266372

Emmanuel Chevallier, Jesús Angulo, Emmanuel K. Kalunga

Publication date: 2 June 2017

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1053566

zbMATH Keywords

Riemannian geometrykernel density estimationWasserstein distanceFisher distance

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Density estimation (62G07) Applications of statistics to biology and medical sciences; meta analysis (62P10) Exact distribution theory in statistics (62E15) Applications of differential geometry to physics (53Z05)

Related Items

Exponential-Wrapped Distributions on Symmetric Spaces ⋮ Kernel density estimation on symmetric spaces of non-compact type ⋮ Wasserstein Riemannian geometry of Gaussian densities ⋮ A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications ⋮ Wrapped Statistical Models on Manifolds: Motivations, The Case SE(n), and Generalization to Symmetric Spaces ⋮ A Nonlocal Denoising Algorithm for Manifold-Valued Images Using Second Order Statistics

Uses Software

• Matrix Means Toolbox

Cites Work

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• Wasserstein geometry of Gaussian measures
• Nonparametric estimation of a probability density on a Riemannian manifold using Fourier expansions
• Möbius deconvolution on the hyperbolic plane with application to impedance density estimation
• Multivariate normal distributions parametrized as a Riemannian symmetric space
• Computing the Karcher mean of symmetric positive definite matrices
• Kernel density estimation on Riemannian manifolds
• A Riemannian framework for tensor computing
• From Euclidean to Riemannian Means: Information Geometry for SSVEP Classification
• Probability Density Estimation on the Hyperbolic Space Applied to Radar Processing
• k-Nearest neighbor density estimation on Riemannian Manifolds
• Riemannian median and its estimation
• Barycenters in the Wasserstein Space
• On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions
• Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices
• Deconvolution Density Estimation on the Space of Positive Definite Symmetric Matrices
• Elementary Differential Topology. (AM-54)
• Optimal Transport