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- W1972801555 abstract "The problem of estimating the intrinsic dimensionality of certain point clouds is of interest in many applications in statistics and analysis of high-dimensional data sets. Our setting is the following: the points are sampled from a manifold M of dimension k, embedded in Ropf <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>D</sup> , with k Lt D, and corrupted by D-dimensional noise. When M is a linear manifold (hyperplane), one may analyse this situation by SVD, hoping the noise would perturb the rank k covariance matrix. When M is a nonlinear manifold, SVD performed globally may dramatically overestimate the intrinsic dimensionality. We discuss a multiscale version SVD that is useful in estimating the intrinsic dimensionality of nonlinear manifolds." @default.
- W1972801555 created "2016-06-24" @default.
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- W1972801555 date "2009-08-01" @default.
- W1972801555 modified "2023-10-01" @default.
- W1972801555 title "Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD" @default.
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- W1972801555 doi "https://doi.org/10.1109/ssp.2009.5278634" @default.
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