ML Anthology

A Kernel View of the Dimensionality Reduction of Manifolds

Jihun Ham, Daniel D. Lee, Sebastian Mika, Bernhard Schölkopf
ICML 2004
doi:10.1145/1015330.1015417 /icml/2004/ham2004icml-kernel/

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.

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Cite

Text

Ham et al. "A Kernel View of the Dimensionality Reduction of Manifolds." International Conference on Machine Learning, 2004. doi:10.1145/1015330.1015417

Markdown

[Ham et al. "A Kernel View of the Dimensionality Reduction of Manifolds." International Conference on Machine Learning, 2004.](https://mlanthology.org/icml/2004/ham2004icml-kernel/) doi:10.1145/1015330.1015417

BibTeX

@inproceedings{ham2004icml-kernel,
  title     = {{A Kernel View of the Dimensionality Reduction of Manifolds}},
  author    = {Ham, Jihun and Lee, Daniel D. and Mika, Sebastian and Schölkopf, Bernhard},
  booktitle = {International Conference on Machine Learning},
  year      = {2004},
  doi       = {10.1145/1015330.1015417},
  url       = {https://mlanthology.org/icml/2004/ham2004icml-kernel/}
}