Header logo is

A kernel view of the dimensionality reduction of manifolds

2004

Conference Paper

ei


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

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: ICML 2004
Event Place: Banff, Alberta, Canada

Address: New York, NY, USA
Note: also appeared as MPI-TR 110
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: PDF

BibTex

@inproceedings{2326,
  title = {A kernel view of the dimensionality reduction of manifolds},
  author = {Ham, J. and Lee, DD. and Mika, S. and Sch{\"o}lkopf, B.},
  booktitle = {Proceedings of the Twenty-First International Conference on Machine Learning},
  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}
}