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Intrinsic Dimensionality Estimation of Submanifolds in Rd Matthias Hein mh@tuebingen.mpg.de
 

Summary: Intrinsic Dimensionality Estimation of Submanifolds in Rd
Matthias Hein mh@tuebingen.mpg.de
Max Planck Institute for Biological Cybernetics, T¨ubingen, Germany
Jean-Yves Audibert audibert@certis.enpc.fr
CERTIS, ENPC, Paris, France
Abstract
We present a new method to estimate the
intrinsic dimensionality of a submanifold M
in Rd
from random samples. The method
is based on the convergence rates of a cer-
tain U-statistic on the manifold. We solve
at least partially the question of the choice
of the scale of the data and can quantify
the influence of the extrinsic curvature of the
manifold. Moreover the proposed method is
easy to implement, can handle large data sets
and performs very well even for small sample
sizes. We compare the proposed method to
two standard estimators on several artificial

  

Source: Audibert, Jean-Yves - Département d'Informatique, École Normale Supérieure

 

Collections: Computer Technologies and Information Sciences