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Conference Paper

A kernel view of the dimensionality reduction of manifolds

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

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

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Citation

Ham, J., Lee DD, Mika, S., & Schölkopf, B. (2004). A kernel view of the dimensionality reduction of manifolds. In Proceedings of the Twenty-First International Conference on Machine Learning (pp. 369-376).


Cite as: http://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.