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Regression on manifolds using kernel dimension reduction

Nilsson, Jens LU ; Sha, Fei and Jordan, Michael I. (2007) 24th International Conference on Machine Learning, ICML 2007 In ACM International Conference Proceeding Series 227. p.697-704
Abstract
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... (More)
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 and image manifolds. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Laplacian eigenmaps, Manifold learning, Kernel dimension reduction, Nonlinear regression
in
ACM International Conference Proceeding Series
volume
227
pages
697 - 704
publisher
ACM
conference name
24th International Conference on Machine Learning, ICML 2007
external identifiers
  • Scopus:34547968745
ISBN
978-1-59593-793-3
DOI
10.1145/1273496.1273584
language
English
LU publication?
yes
id
9ea92558-ca0a-457d-a4c4-6f6476728c1d (old id 643567)
alternative location
http://www.machinelearning.org/proceedings/icml2007/papers/491.pdf
date added to LUP
2007-12-04 16:05:43
date last changed
2016-10-13 04:42:38
@misc{9ea92558-ca0a-457d-a4c4-6f6476728c1d,
  abstract     = {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 and image manifolds.},
  author       = {Nilsson, Jens and Sha, Fei and Jordan, Michael I.},
  isbn         = {978-1-59593-793-3},
  keyword      = {Laplacian eigenmaps,Manifold learning,Kernel dimension reduction,Nonlinear regression},
  language     = {eng},
  pages        = {697--704},
  publisher    = {ARRAY(0x928aa68)},
  series       = {ACM International Conference Proceeding Series},
  title        = {Regression on manifolds using kernel dimension reduction},
  url          = {http://dx.doi.org/10.1145/1273496.1273584},
  volume       = {227},
  year         = {2007},
}