Parameterization of non-linear manifolds

Abstract

In this report we consider the parameterization of low-dimensional manifolds that are specified (approximately) by a set of points very close to the manifold in the original high-dimensional space. Our objective is to obtain a parameterization that is (1-1) and non singular (in the sense that the Jacobian of the map between the manifold and the parameter space is bounded and non singular).

11 pages, 6 figures

References in corpus (1)

• Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment

Cited by in corpus (1)

• Manifold Coordinates with Physical Meaning