Abstract:
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What does it mean to learn a manifold? Isomap, Locally Linear Embedding, and Laplacian eigenmaps were proposed as techniques for nonlinear dimension reduction, then Isomap was criticized for solving the parameterization recovery problem under less general conditions than Hessian eigenmaps. We observe that the class of manifolds for which parameterization recovery is possible is extremely small, consisting essentially of Swiss rolls. We then compare Isomap and Hessian eigenmaps with respect to other exploitation tasks that elucidate what manifold learning may-or may not-entail.
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