In this paper we address the problem of high-dimensionality for data that lies on complex manifolds. In high-dimensional spaces, distances between the nearest and farthest neighbour tend to become equal. This behaviour hardens data analysis, such as clustering. We show that distance transformation can be used in an effective way to obtain an embedding space of lower-dimensionality than the orig...

Article history: Available online 29 October 2011

We describe a computer intensive method for linear dimension re duction which minimizes the classi cation error directly Simulated annealing Bohachevsky et al is used to solve this problem The classi cation error is determined by an exact integration We avoid distance or scatter measures which are only surrogates to circumvent the classi cation error Simulations in two dimensions and analytical...

Honeybees determine distance flown by gauging the extent to which the image of the environment moves in the eye as they fly towards their goal. Here we investigate how this visual odometer operates when a bee flies along paths that include a vertical component. By training bees to fly to a feeder along tunnels of various three-dimensional configurations, we find that the odometric signal depend...

A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension of Γ is the smallest size of a resolving set for Γ. Much attention has been paid to the metric dimension of distance-regular graphs. Work of Babai from the early 1980s yields general bounds on the metric dimens...

We give the maximal distance between a copula and itself when the argument is permuted for arbitrary dimension, generalizing a result for dimension two by Nelsen (2007); Klement and Mesiar (2006). Furthermore, we establish a subset of [0, 1] in which this bound might be attained. For each point in this subset we present a copula and a permutation, for which the distance in this point is maximal...

Images containing faces are essential to intelligent visionbased human computer interaction, and research efforts in face processing include face recognition, face tracking, pose estimation, and expression recognition. The rapidly expanding research in face processing is based on the premise that information about a user’s identity, state, and intent can be extracted from images and that comput...

The metric dimension of a graph G is the size of a smallest subset L ⊆ V (G) such that for any x, y ∈ V (G) there is a z ∈ L such that the graph distance between x and z differs from the graph distance between y and z. Even though this notion has been part of the literature for almost 40 years, the computational complexity of determining the metric dimension of a graph is still very unclear. Es...

The goal of a hub-based distance labeling scheme for a network G = (V,E) is to assign a small subset S(u) ⊆ V to each node u ∈ V , in such a way that for any pair of nodes u, v, the intersection of hub sets S(u) ∩ S(v) contains a node on the shortest uv-path. The existence of small hub sets, and consequently efficient shortest path processing algorithms, for road networks is an empirical observ...

This paper offers a methodological contribution for computing the distance between two empirical distributions in an Euclidean space of very large dimension. We propose to use decision trees instead of relying on standard quantifi10 cation of the feature space. Our contribution is two-fold: We first define a new distance between empirical distributions, based on the Kullback-Leibler (KL) diverg...