The Globally Linear Embedding Algorithm
- 10.2991/iccia.2012.42How to use a DOI?
- Locally Linear Embedding,Dimension Reduction , Globally Linear Embedding
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.
- © 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/).
Cite this article
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 -