Laplacian Eigenmaps for Dimensionality Reduction and Data Representation

DOI Web Site 被引用文献55件
  • Mikhail Belkin
    Department of Mathematics, University of Chicago, Chicago, IL 60637, U.S.A.,
  • Partha Niyogi
    Department of Computer Science and Statistics, University of Chicago, Chicago, IL 60637 U.S.A.,

説明

<jats:p> One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed. </jats:p>

収録刊行物

  • Neural Computation

    Neural Computation 15 (6), 1373-1396, 2003-06-01

    MIT Press - Journals

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