LDR-LLE: LLE with low-dimensional neighborhood representation

Yair Goldberg, Ya'Acov Ritov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique that is widely used for its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in a low-dimensional embedding. We show that the reconstruction weights computed by LLE capture the high-dimensional structure of the neighborhoods, and not the low-dimensional manifold structure. Consequently, the weight vectors are highly sensitive to noise. Moreover, this causes LLE to converge to a linear projection of the input, as opposed to its non-linear embedding goal. To resolve both of these problems, we propose to compute the weight vectors using a low-dimensional neighborhood representation. We call this technique LDR-LLE. We present numerical examples of the perturbation and linear projection problems, and of the improved outputs resulting from the low-dimensional neighborhood representation.

Original languageEnglish
Title of host publicationAdvances in Visual Computing - 4th International Symposium, ISVC 2008, Proceedings
Pages43-54
Number of pages12
EditionPART 2
DOIs
StatePublished - 2008
Externally publishedYes
Event4th International Symposium on Visual Computing, ISVC 2008 - Las Vegas, NV, United States
Duration: 1 Dec 20083 Dec 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume5359 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th International Symposium on Visual Computing, ISVC 2008
Country/TerritoryUnited States
CityLas Vegas, NV
Period1/12/083/12/08

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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