Fréchet Embeddings of Negative Type Metrics

Abstract

We show that every n-point metric of negative type (in particular, every n-point subset of L 1) admits a Fréchet embedding into Euclidean space with distortion \(O(\sqrt{\log n}\cdot \log \log n)\) , a result which is tight up to the O(log log n) factor, even for Euclidean metrics. This strengthens our recent work on the Euclidean distortion of metrics of negative into Euclidean space.