Nonlinear Dimensionality Reduction by Locally Linear Embedding

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 embeddin...

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Bibliographic Details
Published in:Science (American Association for the Advancement of Science) 2000-12, Vol.290 (5500), p.2323-2326
Main Authors: Roweis, Sam T., Saul, Lawrence K.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Analysis
Artificial Intelligence
Biological and medical sciences
Coordinate systems
Cost functions
Data Analysis
Dimensionality
Dimensionality reduction
Embeddings
Face
Fundamental and applied biological sciences. Psychology
Humans
Mathematical manifolds
Mathematical vectors
Mathematics
Matrices
Multidimensional Scaling
Neighborhoods
Neurology
Pattern Recognition, Visual
Principal components analysis
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics. Statistics. Methodology
Semantics
Statistics. Mathematics
Visual perception
Visualization
Visualization (Mental images)
Visualization (Psychology)
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Summary: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.
ISSN:0036-8075
1095-9203
DOI:10.1126/science.290.5500.2323