When dealing with pattern recognition problems one encounters different types of prior knowledge. It is important to incorporate such knowledge into the classification method at hand. A common prior knowledge is that many datasets are on some kinds of manifolds. Distance-based classification methods can make use of this by a modified distance measure called geodesic distance. We introduce a new...

In the theory of belief functions, distances between basic belief assignments are very important in many applications like clustering, conflict measuring, reliability estimation. In the discrete domain, many measures have been proposed, however, distance between continuous belief functions have been marginalized due to the nature of these functions. In this paper, we propose an adaptation inspi...

Facility location problems have always been studied with the assumption that the edge lengths in the network are static and do not change over time. The underlying network could be used to model a city street network for emergency facility location/hospitals, or an electronic network for locating information centers. In any case, it is clear that due to tra c congestion the traversal time on li...

Default reasoning has become an important topic in software engineering. In particular, defaults can be used to revise speci cations, to enhance reusability of existing systems, and to allow a more economic description of systems. In this paper we develop a framework for default speci cations of reactive systems. We present a formalisation of non-monotonicity in temporal logic based on the noti...

Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also present some computational properties and examples.

I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a nonnegative linear combination of Gegenbauer polynomials. This fact play a crucial role in Delsarte’s method for finding bounds for the density of sphere packings on spheres and Euclidean spaces. One of the most excited applications of Delsarte’s method is a solution of the kissing ...

An new paradigm for computing intrinsic distance functions and geodesics on sub-manifolds of given by point clouds is introduced in this paper. The basic idea is that, as shown here, intrinsic distance functions and geodesics on general co-dimension sub-manifolds of can be accurately approximated by extrinsic Euclidean ones computed inside a thin offset band surrounding the manifold. This permi...

the aim of this paper is to establish random coincidence point results for weakly increasing random operators in the setting of ordered metric spaces by using generalized altering distance functions. our results present random versions and extensions of some well-known results in the current literature.

We address the problem of learning distance metrics using side-information in the form of groups of "similar" points. We propose to use the RCA algorithm, which is a simple and efficient algorithm for learning a full ranked Mahalanobis metric (Shental et al., 2002). We first show that RCA obtains the solution to an interesting optimization problem, founded on an information theoretic basis. If ...

We describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps: Construction of the signed distance function (i.e. redistancing) to the interface, and convolution with a suitable kernel. These algorithms can be seen as variants of Merriman, Bence, and Osher’s threshold dynamics [25]. The new algorithms proposed here preserve the computat...