PT - JOURNAL ARTICLE
AU - Roweis, Sam T.
AU - Saul, Lawrence K.
TI - Nonlinear Dimensionality Reduction by Locally Linear Embedding
AID - 10.1126/science.290.5500.2323
DP - 2000 Dec 22
TA - Science
PG - 2323--2326
VI - 290
IP - 5500
4099 - http://science.sciencemag.org/content/290/5500/2323.short
4100 - http://science.sciencemag.org/content/290/5500/2323.full
SO - Science2000 Dec 22; 290
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.