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
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[1] DOI: 10.4310/CAG.2000.v8.n5.a2 · Zbl 1001.58022
[2] DOI: 10.1109/43.144852 · Zbl 05448228
[3] DOI: 10.2307/1969840 · Zbl 0058.37703
[4] DOI: 10.2307/1969989 · Zbl 0070.38603
[5] DOI: 10.1126/science.290.5500.2323
[6] DOI: 10.1162/089976698300017467
[7] DOI: 10.1126/science.290.5500.2268
[8] DOI: 10.1016/0956-0521(91)90014-V
[9] DOI: 10.1126/science.290.5500.2319
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