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Laplacian Eigenmaps for Dimensionality Reduction and Data Representation (2002) [272 citations — 7 self]

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@ARTICLE{Belkin02laplacianeigenmaps,
    author = {Mikhail Belkin and Partha Niyogi},
    title = {Laplacian Eigenmaps for Dimensionality Reduction and Data Representation},
    journal = {Neural Computation},
    year = {2002},
    volume = {15},
    pages = {1373--1396}
}

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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.

Citations

2189	Neural networks – a comprehensive foundation – Haykin - 1994
1142	Normalized cuts and image segmentation – Shi, Malik
744	A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science, Vol 290 – Tenenbaum, Langford - 2000
565	Nonlinear Component Analysis as a Kernel Eigenvalue Problem – Schölkopf, Smola, et al. - 1998
465	On spectral clustering: Analysis and an algorithm – Ng, Jordan, et al. - 2001
179	Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering – Belkin, Niyogi - 2001
92	Diffusion kernels on graphs and other discrete input spaces – Kondor, Lafferty - 2002
53	Graph approximations to geodesics on embedded manifolds – Bernstein, Silva, et al. - 2000
45	Nonlinear Dimensionality Reduction by Locally – Roweis, Saul - 2000
34	The imbedding problem for riemannian manifolds – Nash - 1956
14	Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs – Chung, Grigor'yan, et al. - 2000
9	The Laplacian on a Riemmannian Manifold – Rosenberg - 1997
2	Dimensionality Reduction Techniques for – Indyk - 2001
1	Unsupervised Learning of Curved – Silva, Tenenbaum - 2002