Title: Contour approximation of data, with applications

Speaker: Adi Ben-Israel

Abstract:

Given a set of points S in R^n (the data), a contour approximation of S is a function that captures most points of S in its lower level sets, [1]. 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, [2], a result since then confirmed for many species. The harmonic mean of distances, or resistances, also features in inverse distance weighted interpolation [3], clustering [4], 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.

References

[1] M. Arav, Contour approximation of data, J. Math. Inequalities 2(2008), 161-167

[2] K.R. Dixon and J.A. Chapman, Harmonic mean measure of animal activity areas, Ecology 61(1980), 1040-1044

[3] D. Shepard, A 2-dimensional interpolation function for irregularly-spaced data, Proceedings of the 1968 ACM Nat. Conference, pp. 517-524

[4] M. Teboulle, A unified continuous optimization frame work to center-based clustering methods, J. of Machine Learning 8(2007) 65-102