PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Intrinsic Dimensionality Estimation of Submanifolds in Euclidean Space
Matthias Hein, Jean-Yves Audibert and Ulrike Von Luxburg
In: ICML 2005, 7-11 Aug 2005, Bonn, Germany.

Abstract

We present a new method to estimate the intrinsic dimensionality of a submanifold M in Euclidean space from random samples. The method is based on the convergence rates of a certain U-statistic on the manifold. We solve at least partially the question of the choice of the scale of the data. 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 as well as real data sets.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1596
Deposited By:Matthias Hein
Deposited On:28 November 2005