Locating Local Extrema under Interval Uncertainty: Multi-D Case

Authors

Karen Villaverde, New Mexico State University - Main CampusFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

5-2012

Comments

Technical Report: UTEP-CS-12-05a

Published in Proceedings of the 2012 Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2012, Berkeley, California, August 6-8, 2012.

Abstract

In many practical situations, we need to locate local maxima and/or local minima of a function which is only know with interval uncertainty. For example, in radioastronomy, components of a radiosource are usually identified by locations at which the observed brightness reaches a local maximum. In clustering, different clusters are usually identified with local maxima of the probability density function (describing the relative frequency of different combinations of values). In the 1-D case, a feasible (polynomial-time) algorithm is known for locating local extrema under interval (and fuzzy) uncertainty. In this paper, we extend this result to the general multi-dimensional case.