On lipschitz embedding of finite metric spaces in Hilbert space
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It is shown that anyn point metric space is up to logn lipeomorphic to a subset of Hilbert space. We also exhibit an example of ann point metric space which cannot be embedded in Hilbert space with distortion less than (logn)/(log logn), showing that the positive result is essentially best possible. The methods used are of probabilistic nature. For instance, to construct our example, we make use of random graphs.
KeywordsHilbert Space Riemannian Manifold Random Graph Probabilistic Nature Embedding Problem
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