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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...