Laplacian eigenmaps for dimensionality reduction and data representation. (English) Zbl 1085.68119

Summary: 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.


68T05 Learning and adaptive systems in artificial intelligence
Full Text: DOI


[1] DOI: 10.4310/CAG.2000.v8.n5.a2 · Zbl 1001.58022 · doi:10.4310/CAG.2000.v8.n5.a2
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