Adi Ben-Israel, Rutgers University

Abstract

Given a set of points S in Rn (the data), a contour approximation of S is a function that captures most points of S in its lower level sets, A concrete application is the home range of an animal population, or the territory occupied by it, shown in 1980 by Dixon and Chapman to involve the harmonic mean of certain distances, a result since then confirmed for many species. The harmonic mean of distances, or resistances, also features in inverse distance weighted interpolation clustering, parallel circuits and multi-facility location. This lecture gives an axiomatic framework, and a probabilistic optimization model that unifies the above results, a model applied successfully to clustering and classification.

Joint work with Tsvetan Asamov and Cem Iyigun