Nonlocal estimation of manifold structure.

Full Abstract

We claim and present arguments to the effect that a large class of manifold learning algorithms that are essentially local and can be framed as kernel learning algorithms will suffer from the curse of dimensionality, at the dimension of the true underlying manifold. This observation invites an exploration of nonlocal manifold learning algorithms that attempt to discover shared structure in the tangent planes at different positions. A training criterion for such an algorithm is proposed, and experiments estimating a tangent plane prediction function are presented, showing its advantages with respect to local manifold learning algorithms:
it is able to generalize very far from training data (on learning handwritten character image rotations), where local nonparametric methods fail.

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Author information

Author/s: Bengio, Yoshua (Y); Monperrus, Martin (M); Larochelle, Hugo (H);

Affiliation: bengioy(-atsign-)iro.umontreal.ca

Journal and publication information

Publication Type: Comparative Study; Journal Article; Research Support, Non-U.S. Gov't

Journal: Neural computation (Neural Comput), published in United States. (Language: eng)

Reference: 2006-Oct; vol 18 (issue 10) : pp 2509-28

Dates: Created 2006/08/15; Completed 2006/11/01; Revised 2006/11/15;

PMID: 16907635, status: MEDLINE (last retrieval date: 12/26/2008)

Sourced from the National Library of Medicine. Abstract text and other information may be subject to copyright.

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MeSH headings (categories)

This article was linked to the MESH Headings shown below.

Learning - physiology
Nonlinear Dynamics
Pattern Recognition, Automated - methods

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