Learning by distances

We initiate the study of spanners under the Hausdorff and Fréchet distances. Let S be a set of points in R d and ε a non-negative real number. A subgraph H of the Euclidean graph over S is an ε-Hausdorff-spanner (resp., an ε-Fréchet-spanner) of S,...

• We initiate the study of spanners under the Hausdorff and Fréchet distances.
• We show that any t-spanner of a planar point-set S is a f(t)-Hausdorff-spanner and a g(t)-Fréchet spanner.
• We prove that for any t > 1, there exist a set ...

A model of learning by distances is presented. In this model a concept is a point in a metric space. At each step of the learning process the student guesses a hypothesis and receives from the teacher an approximation of its distance to the target. A ...

In a previously reported work, a distance function was proposed which defines the distance between any pair of points as the weighted sum of their ordered coordinate differences. We call this distance function in this work as linear combination form of ...