Nonlinear Dimensionality Reduction by Locally Linear Embedding

Title: Nonlinear Dimensionality Reduction by Locally Linear Embedding
Creator(s): Roweis, Sam T.; Saul, Lawrence K.
Date: 2000
Is Part Of: Science
Volume: 290
Issue: 5500
Pages: 2323-2326
Language: eng
DOI: https://www.science.org/doi/10.1126/science.290.5500.2323
Zotero BiDiAr: https://www.zotero.org/groups/5293298/bidiar/items/QFPCC4L8item-list
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 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.

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