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Laplacian Eigenmaps for Dimensionality Reduction and Data Representation (2003)

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by Mikhail Belkin , Partha Niyogi
Citations:1226 - 15 self
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BibTeX

@MISC{Belkin03laplacianeigenmaps,
    author = {Mikhail Belkin and Partha Niyogi},
    title = { Laplacian Eigenmaps for Dimensionality Reduction and Data Representation},
    year = {2003}
}

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Abstract

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 ap-proach to nonlinear dimensionality reduction that has locality-preserving properties and a natural connection to clustering. Some potential applications and illustrative examples are discussed.

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