Nonlinear Dimensionality Reduction by Locally Linear Embedding
Abstract
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 highdimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes lowdimensional, neighborhoodpreserving embeddings of highdimensional 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.
 Publication:

Science
 Pub Date:
 December 2000
 DOI:
 10.1126/science.290.5500.2323
 Bibcode:
 2000Sci...290.2323R
 Keywords:

 COMP/MATH