Nonlinear dimensionality reduction by locally linear embedding.
Sam Roweis & Lawrence Saul.
Science v.290 no.5500, Dec.22, 2000. pp.2323--2326.
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.