Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD

Anna V. Little, Jason Lee, Yoon Mo Jung, Mauro Maggioni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

29 Scopus citations

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.

Original languageEnglish (US)
Title of host publication2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09
Pages85-88
Number of pages4
DOIs
StatePublished - Dec 25 2009
Externally publishedYes
Event2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09 - Cardiff, United Kingdom
Duration: Aug 31 2009Sep 3 2009

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings

Other

Other2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09
CountryUnited Kingdom
CityCardiff
Period8/31/099/3/09

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

Keywords

  • High dimensional data
  • Intrinsic dimensionality
  • Manifolds
  • Multiscale analysis
  • PCA
  • Point clouds
  • SVD
  • Sample covariance

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  • Cite this

    Little, A. V., Lee, J., Jung, Y. M., & Maggioni, M. (2009). Estimation of intrinsic dimensionality of samples from noisy low-dimensional manifolds in high dimensions with multiscale SVD. In 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09 (pp. 85-88). [5278634] (IEEE Workshop on Statistical Signal Processing Proceedings). https://doi.org/10.1109/SSP.2009.5278634