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Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery
Non-linear dimensionality reduction Riemannian metric estimation the problem geometric discovery
2013/6/14
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degre...
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...
Riemannian statistics geometry: A counterpart approach of inference geometry
Geometrical Methods in Statistics
2011/7/19
Riemannian statistics geometry is proposed in this work as a counterpart approach of inference geometry.
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...