The Globally Linear Embedding Algorithm

DOI

10.2991/iccia.2012.42How to use a DOI?

Keywords

Locally Linear Embedding,Dimension Reduction , Globally Linear Embedding

Abstract

LLE is a very effective non-linear dimension reduction algorithm and widely explored in machine learning, pattern recognition, data mining and etc. ‘Locally linear, Globally non-linear’ has always been regarded as the features and advantages of LLE. However, the theoretical derivation presented in this paper shows that when the size of neighborhood is larger than the dimension of the space in which the data are presented, LLE is no longer ‘global nonlinear’ and almost has the same effect as PCA in dimensionality reduction. At present, a lot of literatures on LLE verify their results on Swiss Roll, Punctured Sphere, Twin Peaks, etc. These manifolds are presented in the three-dimensional Euclidean space and the size of neighborhood is always larger than three to prevent too small to be effective. But in these cases, LLE cannot play its advantage of nonlinearity.

Copyright

© 2013, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Jieyun Xia
AU  - Shuaibin Lian
PY  - 2014/05
DA  - 2014/05
TI  - The Globally Linear Embedding Algorithm
BT  - Proceedings of the 2012 2nd International Conference on Computer and Information Application (ICCIA 2012)
PB  - Atlantis Press
SP  - 172
EP  - 175
SN  - 1951-6851
UR  - https://doi.org/10.2991/iccia.2012.42
DO  - 10.2991/iccia.2012.42
ID  - Xia2014/05
ER  -