Math @ Duke

Publications [#243804] of Mauro Maggioni
Papers Published
 Little, AV; Lee, J; Jung, YM; Maggioni, M, Estimation of intrinsic dimensionality of samples from noisy lowdimensional manifolds in high dimensions with multiscale SVD,
IEEE Workshop on Statistical Signal Processing Proceedings
(2009),
pp. 8588 [doi]
(last updated on 2018/09/22)
Abstract: The problem of estimating the intrinsic dimensionality of certain point clouds is of interest in many applications in statistics and analysis of highdimensional data sets. Our setting is the following: the points are sampled from a manifold M of dimension k, embedded in ℝD, with k < D, and corrupted by Ddimensional 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. © 2009 IEEE.


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