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ICML
2007
IEEE

Regression on manifolds using kernel dimension reduction

9 years 12 months ago
Regression on manifolds using kernel dimension reduction
We study the problem of discovering a manifold that best preserves information relevant to a nonlinear regression. Solving this problem involves extending and uniting two threads of research. On the one hand, the literature on sufficient dimension reduction has focused on methods for finding the best linear subspace for nonlinear regression; we extend this to manifolds. On the other hand, the literature on manifold learning has focused on unsupervised dimensionality reduction; we extend this to the supervised setting. Our approach to solving the problem involves combining the machinery of kernel dimension reduction with Laplacian eigenmaps. Specifically, we optimize cross-covariance operators in kernel feature spaces that are induced by the normalized graph Laplacian. The result is a highly flexible method in which no strong assumptions are made on the regression function or on the distribution of the covariates. We illustrate our methodology on the analysis of global temperature data...
Jens Nilsson, Fei Sha, Michael I. Jordan
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2007
Where ICML
Authors Jens Nilsson, Fei Sha, Michael I. Jordan
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