Non-asymptotic analysis of tangent space perturbation
نویسندگان
چکیده
منابع مشابه
Non-Asymptotic Analysis of Tangent Space Perturbation
Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as it returns an optimal basis in the case of noise-free samples from a linear su...
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Article history: Received 21 August 2007 Accepted 12 September 2008 Available online 22 October 2008 Submitted by R.A. Brualdi AMS classification: 15A60 65F99
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Given an n-sample drawn on a submanifold M ⊂ R, we derive optimal rates for the estimation of tangent spaces TXM , the second fundamental form II X , and the submanifold M . After motivating their study, we introduce a quantitative class of C-submanifolds in analogy with Hölder classes. The proposed estimators are based on local polynomials and allow to deal simultaneously with the three proble...
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Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...
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ژورنال
عنوان ژورنال: Information and Inference: A Journal of the IMA
سال: 2014
ISSN: 2049-8772,2049-8764
DOI: 10.1093/imaiai/iau004