Regression on manifolds using kernel dimension reduction
(2007) 24th International Conference on Machine Learning, ICML 2007 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:
https://lup.lub.lu.se/record/643567
- author
- Nilsson, Jens LU ; Sha, Fei and Jordan, Michael I.
- organization
- publishing date
- 2007
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Laplacian eigenmaps, Manifold learning, Kernel dimension reduction, Nonlinear regression
- host publication
- ACM International Conference Proceeding Series
- volume
- 227
- pages
- 697 - 704
- publisher
- Association for Computing Machinery (ACM)
- conference name
- 24th International Conference on Machine Learning, ICML 2007
- conference location
- Corvalis, OR, United States
- conference dates
- 2007-06-20 - 2007-06-24
- 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
- 2016-04-04 10:53:23
- date last changed
- 2022-03-23 08:44:29
@inproceedings{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.}},
booktitle = {{ACM International Conference Proceeding Series}},
isbn = {{978-1-59593-793-3}},
keywords = {{Laplacian eigenmaps; Manifold learning; Kernel dimension reduction; Nonlinear regression}},
language = {{eng}},
pages = {{697--704}},
publisher = {{Association for Computing Machinery (ACM)}},
title = {{Regression on manifolds using kernel dimension reduction}},
url = {{http://dx.doi.org/10.1145/1273496.1273584}},
doi = {{10.1145/1273496.1273584}},
volume = {{227}},
year = {{2007}},
}