A kernel view of the dimensionality reduction of manifolds
2004
Conference Paper
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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 |
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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}, doi = {} } |