A kernel view of the dimensionality reduction of manifolds

Ham, J; Lee, DD; Mika, S; Schölkopf, B

doi:10.1145/1015330.1015417

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A kernel view of the dimensionality reduction of manifolds

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Schölkopf, B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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https://repository.upenn.edu/cgi/viewcontent.cgi?article=1100&context=ese_papers
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Citation

Ham, J., Lee, D., Mika, S., & Schölkopf, B. (2004). A kernel view of the dimensionality reduction of manifolds. In R. Greiner, & D. Schuurmans (Eds.), ICML '04: Twenty-First International Conference on Machine Learning (pp. 369-376). New York, NY, USA: ACM Press.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-F3AF-6

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.