Empirical Inference
Conference Paper
2004
A kernel view of the dimensionality reduction of manifolds
We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.
| Author(s): | Ham, J. and Lee, DD. and Mika, S. and Schölkopf, B. |
| Book Title: | Proceedings of the Twenty-First International Conference on Machine Learning |
| Pages: | 369-376 |
| Year: | 2004 |
| Day: | 0 |
| Editors: | CE Brodley |
| Publisher: | ACM |
| Bibtex Type: | Conference Paper (inproceedings) |
| Address: | New York, NY, USA |
| Event Name: | ICML 2004 |
| Event Place: | Banff, Alberta, Canada |
| Electronic Archiving: | grant_archive |
| Note: | also appeared as MPI-TR 110 |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@inproceedings{2326,
title = {A kernel view of the dimensionality reduction of manifolds},
booktitle = {Proceedings of the Twenty-First International Conference on Machine Learning},
abstract = {We interpret several well-known algorithms for dimensionality reduction of manifolds as kernel methods. Isomap, graph Laplacian eigenmap, and locally linear embedding (LLE) all utilize local neighborhood information to construct a global embedding of the manifold. We show how all three algorithms can be described as kernel PCA on specially constructed
Gram matrices, and illustrate the similarities and differences between the algorithms with representative examples.},
pages = {369-376},
editors = {CE Brodley},
publisher = {ACM},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
address = {New York, NY, USA},
year = {2004},
note = {also appeared as MPI-TR 110},
slug = {2326},
author = {Ham, J. and Lee, DD. and Mika, S. and Sch{\"o}lkopf, B.}
}