Parameterization of non-linear manifolds
arXiv:1208.52466 citationsh-index: 47
Originality Synthesis-oriented
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Provides a theoretical framework for manifold parameterization, relevant for dimensionality reduction and data analysis.
The paper addresses the problem of parameterizing low-dimensional manifolds from noisy point samples in high-dimensional space, achieving a 1-1 and non-singular mapping with bounded Jacobian.
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).