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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.
