Some Recent Advances in Multiscale Geometric Analysis of Point Clouds

  • Guangliang Chen
  • Anna V. Little
  • Mauro Maggioni
  • Lorenzo Rosasco
Chapter
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Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We discuss recent work based on multiscale geometric analyis for the study of large data sets that lie in high-dimensional spaces but have low-dimensional structure. We present three applications: the first one to the estimation of intrinsic dimension of sampled manifolds, the second one to the construction of multiscale dictionaries, called Geometric Wavelets, for the analysis of point clouds, and the third one to the inference of point clouds modeled as unions of multiple planes of varying dimensions.

Keywords

Point Cloud Singular Value Decomposition Intrinsic Dimension Principle Component Analysis Spectral Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Guangliang Chen
  • Anna V. Little
  • Mauro Maggioni
    • 1
  • Lorenzo Rosasco
  1. 1.Duke UniversityDurhamUSA

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