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NIPS
2001
13 years 6 months ago
Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering
Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motiva...
Mikhail Belkin, Partha Niyogi
CVPR
2008
IEEE
14 years 6 months ago
Large-scale manifold learning
This paper examines the problem of extracting lowdimensional manifold structure given millions of highdimensional face images. Specifically, we address the computational challenge...
Ameet Talwalkar, Sanjiv Kumar, Henry A. Rowley
FTML
2010
159views more  FTML 2010»
13 years 3 months ago
Dimension Reduction: A Guided Tour
We give a tutorial overview of several geometric methods for dimension reduction. We divide the methods into projective methods and methods that model the manifold on which the da...
Christopher J. C. Burges
ICML
2007
IEEE
14 years 5 months ago
Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian Eigenmaps
Non-linear dimensionality reduction of noisy data is a challenging problem encountered in a variety of data analysis applications. Recent results in the literature show that spect...
Samuel Gerber, Tolga Tasdizen, Ross T. Whitaker
ICML
2005
IEEE
14 years 5 months ago
Analysis and extension of spectral methods for nonlinear dimensionality reduction
Many unsupervised algorithms for nonlinear dimensionality reduction, such as locally linear embedding (LLE) and Laplacian eigenmaps, are derived from the spectral decompositions o...
Fei Sha, Lawrence K. Saul