Euclidean metric and flat metric outside a compact set

Metric and Euclidean TSP

Hybrid Euclidean-and-Riemannian Metric Learning for Image Set Classification

We propose a novel hybrid metric learning approach to combine multiple heterogenous statistics for robust image set classification. Specifically, we represent each set with multiple statistics – mean, covariance matrix and Gaussian distribution, which generally complement each other for set modeling. However, it is not trivial to fuse them since the mean vector with d-dimension often lies in Eu...

Euclidean vs Graph Metric

The theory of sparse graph limits concerns itself with versions of local convergence and global convergence, see e.g. [41]. Informally, in local convergence we look at a large neighborhood around a random uniformly chosen vertex in a graph and in global convergence we observe the whole graph from afar. In this note rather than surveying the general theory we will consider some concrete examples...

Metric Transforms and Euclidean Embeddings

It is proved that if 0 < c < 0.72/« then for any «-point metric space (X, d), the metric space (X,dc) is isometrically embeddable into a Euclidean space. For 6-point metric space, c = j log2 | is the largest exponent that guarantees the existence of isometric embeddings into a Euclidean space. Such largest exponent is also determined for all «-point graphs with "truncated distance".

Near-Optimal (Euclidean) Metric Compression

The metric sketching problem is defined as follows. Given a metric on n points, and > 0, we wish to produce a small size data structure (sketch) that, given any pair of point indices, recovers the distance between the points up to a 1 + distortion. In this paper we consider metrics induced by `2 and `1 norms whose spread (the ratio of the diameter to the closest pair distance) is bounded by Φ >...