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Science 22 December 2000:
Vol. 290. no. 5500, pp. 2323 - 2326
DOI: 10.1126/science.290.5500.2323
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Reports

Nonlinear Dimensionality Reduction by Locally Linear Embedding

Sam T. Roweis,1 and Lawrence K. Saul2

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.

1 Gatsby Computational Neuroscience Unit, University College London, 17 Queen Square, London WC1N 3AR, UK.
2 AT&T Lab--Research, 180 Park Avenue, Florham Park, NJ 07932, USA.
E-mail: roweis{at}gatsby.ucl.ac.uk (S.T.R.); lsaul{at}research.att.com (L.K.S.)

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