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Embedding Riemannian Manifolds by the Heat Kernel of the Connection Laplacian
Embedding Riemannian Manifolds Heat Kernel Connection Laplacian
2013/6/17
Given a class of closed Riemannian manifolds with prescribed geometric conditions, we introduce an embedding of the manifolds into $\ell^2$ based on the heat kernel of the Connection Laplacian associa...
Tangent space estimation for smooth embeddings of Riemannian manifolds
Riemannian manifolds tangent space estimation manifold sampling manifold learning Chernoff bounds for sums of random matrices singular value perturbation.
2012/9/17
Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require ...
k-Nearest neighbor density estimation on Riemannian Manifolds
Asymptotic results Density estimation Meteorological applications
2011/7/6
In this paper, we consider a k-nearest neighbor kernel type estimator when the random variables belong in a Riemannian manifolds.
Partially linear models on Riemannian manifolds
Nonparametric estimation Partly linear models Riemannian manifolds
2010/3/11
In partially linear models the dependence of the response y on (xt, t) is modeled through the relationship
y = xt +g(t)+" where " is independent of (xt, t). In this paper, estimators of g are constr...
A Bayesian approach to the estimation of maps between riemannian manifolds
Bayesian problems Bayes estimators Minimax estimators riemannian geometry sub-riemannian geometry
2010/4/29
Let γ be a smooth compact oriented manifold without boundary,
imbedded in a euclidean space Es, and let γ be a smooth map of into
a Riemannian manifold . An unknown state θ 2 is observed via X...