| Monotone Maps, Sphericity and Bounded Second Eigenvalue (2004) | |||||||||||||||||
Abstract | |||||||||||||||||
| We consider monotone embeddings of a nite metric space into low dimensional normed space. That is, embeddings that respect the order among the distances in the original space. Our main interest is in embeddings into Euclidean spaces. We observe that any metric on n points can be embedded into l 2 , while, (in a sense to be made precise later), for almost every n-point metric space, every monotone map must be into a space of dimension n) (Lemma 3). | |||||||||||||||||
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