Metric Embeddings with Relaxed Guarantees

Supervised Metric Learning with Generalization Guarantees

In recent years, the crucial importance of metrics in machine learning algorithms has led to anincreasing interest in optimizing distance and similarity functions using knowledge from training data to makethem suitable for the problem at hand. This area of research is known as metric learning. Existing methodstypically aim at optimizing the parameters of a given metric with respect ...

Computational metric embeddings

We study the problem of computing a low-distortion embedding between two metric spaces. More precisely given an input metric space M we are interested in computing in polynomial time an embedding into a host space M ′ with minimum multiplicative distortion. This problem arises naturally in many applications, including geometric optimization, visualization, multi-dimensional scaling, network spa...

Csc2414 -metric Embeddings

According to Johnson-Lindenstrauss Lemma there is a projection from a Euclidian space to a subspace of dimension O( logn 2 ), that scales distances within a factor of 1 + . A natural extension of this result suggests the preservation of other geometric characteristics like angles, areas and volumes of simplexes spanned by many vectors. In this direction we see how to obtain similar results when...

Metric Embeddings and Lipschitz Extensions

Geometric embeddings of metric spaces