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      Nonlinear dimensionality reduction by locally linear embedding.

      Science (New York, N.Y.)
      Algorithms, Artificial Intelligence, Face, Humans, Mathematics, Pattern Recognition, Visual

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          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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          Author and article information

          Journal
          11125150
          10.1126/science.290.5500.2323

          Chemistry
          Algorithms,Artificial Intelligence,Face,Humans,Mathematics,Pattern Recognition, Visual
          Chemistry
          Algorithms, Artificial Intelligence, Face, Humans, Mathematics, Pattern Recognition, Visual

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