@inproceedings{82b2fb0e8b3a44299ac9ee721cebbfce,
title = "Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD",
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 ℝD, with k < D, and corrupted by D-dimensional noise. When M is a linear manifold (hy-perplane), 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.",
keywords = "High dimensional data, Intrinsic dimensionality, Manifolds, Multiscale analysis, PCA, Point clouds, SVD, Sample covariance",
author = "Little, {Anna V.} and Jason Lee and Jung, {Yoon Mo} and Mauro Maggioni",
year = "2009",
doi = "10.1109/SSP.2009.5278634",
language = "English (US)",
isbn = "9781424427109",
series = "IEEE Workshop on Statistical Signal Processing Proceedings",
pages = "85--88",
booktitle = "2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09",
note = "2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09 ; Conference date: 31-08-2009 Through 03-09-2009",
}