HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Bengio, Y. Articles by Larochelle, H. Search for Related Content PubMed PubMed Citation Articles by Bengio, Y. Articles by Larochelle, H.

Nonlocal Estimation of Manifold Structure

bengioy{at}iro.umontreal.ca

Martin Monperrus

martin.monperrus{at}laposte.net

Hugo Larochelle

larochech{at}iro.umontreal.ca Département d'Informatique et Recherche Opérationnelle, Centre de Recherches Mathématiques, Université de Montréal, Montréal, Québec, Canada, H3C 3J7

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.