RT Journal Article
SR Electronic
T1 Nonlinear Dimensionality Reduction by Locally Linear Embedding
JF Science
JO Science
FD American Association for the Advancement of Science
SP 2323
OP 2326
DO 10.1126/science.290.5500.2323
VO 290
IS 5500
A1 Roweis, Sam T.
A1 Saul, Lawrence K.
YR 2000
UL http://science.sciencemag.org/content/290/5500/2323.abstract
AB Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.