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Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering.
The numerical solutions of the eigenvalue problem for compact integral operators
Kendall E. Atkinson · 1967
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Laplacian eigenmaps and spectral techniques for embedding and clustering
Mikhail Belkin and Partha Niyogi · 2001
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On spectral clustering: Analysis and an algorithm
Andrew Y. Ng, Michael I. Jordan, and Yair Weiss · 2001
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Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
David L. Donoho and Carrie Grimes · 2003
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Self-tuning spectral clustering
Lihi Zelnik-Manor and Pietro Perona · 2004
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Perspectives and challenges to harmonic analysis and geometry in high dimensions: geometric diffusions as a tool for harmonic analysis and structure definition of data
R. R. Coifman · 2005
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From graphs to manifolds - weak and strong pointwise consistency of graph laplacians
Matthias Hein, Jean-Yves Audibert, and Ulrike von Luxburg · 2005
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Convergence of laplacian eigenmaps
Mikhail Belkin and Partha Niyogi · 2006
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From graph to manifold Laplacian: the convergence rate
A. Singer · 2006
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A tutorial on spectral clustering
Ulrike v. L · 2007
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Towards a theoretical foundation for Laplacian-based manifold methods
Mikhail Belkin and Partha Niyogi · 2008
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Consistency of spectral clustering
Ulrike von Luxburg, Mikhail Belkin, and Olivier Bousquet · 2008
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Spectral convergence of the connection laplacian from random samples
Amit Singer and Hau tieng Wu · 2014
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A variational approach to the consistency of spectral clustering
N. G. Trillos and D. Slep · 2015
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Nonparametric bayesian regression on manifolds via brownian motion
X. Wang and G. Lerman · 2015
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