Nonlinear Dimensionality Reduction by Locally Linear Embedding

2000/12/22 by Sam T. Roweis, Lawrence K. Saul · 16 citations
Computer Science · Mathematics · #Face and Expression Recognition #Advanced Vision and Imaging #Image Retrieval and Classification Techniques #Dimensionality reduction #Nonlinear dimensionality reduction #Maxima and minima #Embedding #Cluster analysis #Isomap #Curse of dimensionality #Computer science #Reduction (mathematics) #Diffusion map #Visualization #Artificial intelligence #Pattern recognition (psychology) #Nonlinear system #Algorithm #Mathematics #Physics

paper · doi:10.1126/science.290.5500.2323

openalex publication_date 2000/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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.

Citations

• Dimension Reduction by Local Principal Component Analysis
• Templates for the Solution of Algebraic Eigenvalue Problems

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