A kernel view of the dimensionality reduction of manifolds
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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.
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Postprint version. Copyright ACM, 2004. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 21st International Conference on Machine Learning 2004, Article Number 47. Publisher URL: http://doi.acm.org/10.1145/1015330.1015417
Postprint version. Copyright ACM, 2004. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the 21st International Conference on Machine Learning 2004, Article Number 47. Publisher URL: http://doi.acm.org/10.1145/1015330.1015417