Fréchet Embeddings of Negative Type Metrics

Fréchet Embeddings of Negative Type Metrics

We show that every n-point metric of negative type (in particular, every n-point subset of L1) admits a Fréchet embedding into Euclidean space with distortion O (√ log n · 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.

Distance scales , embeddings , and metrics of negative type ∗

We introduce a new number of new techniques for the construction of low-distortion embeddings of a finite metric space. These include a generic Gluing Lemma which avoids the overhead typically incurred from the näıve concatenation of maps for different scales of a space. We also give a significantly improved and quantitatively optimal version of the main structural theorem of Arora, Rao, and Va...

A Problem Concerning Yamabe-Type Operators of Negative Admissible Metrics

Dual Embeddings and Metrics for Relational Similarity

Abstract. In this work, we study the problem of relational similarity by combining different word embeddings learned from different types of contexts. The word2vec model with linear bag-ofwords contexts can capture more topical and less functional similarity, while the dependency-based word embeddings with syntactic contexts can capture more functional and less topical similarity. We explore to...

Near Isometric Terminal Embeddings for Doubling Metrics

Given a metric space (X, d), a set of terminals K ⊆ X , and a parameter t ≥ 1, we consider metric structures (e.g., spanners, distance oracles, embedding into normed spaces) that preserve distances for all pairs inK ×X up to a factor of t, and have small size (e.g. number of edges for spanners, dimension for embeddings). While such terminal (aka source-wise) metric structures are known to exist...