Physical Sciences and Mathematics Commons^™

Fast Implementation Of Depth Contours Using Topological Sweep, Kim Miller, Suneeta Ramaswami, Peter Rousseeuw, Toni Sellarès, Diane Souvaine, Ileana Streinu, Anja Struyf

Computer Science: Faculty Publications

The concept of location depth was introduced in statistics as a way to extend the univariate notion of ranking to a bivariate configuration of data points. It has been used successfully for robust estimation, hypothesis testing, and graphical display. These reguire the computation of depth regions, which form a collection of nested polygons. The center of the deepest region is called the Tukey median. The only available implemented algorithms for the depth contours and the Tukey median are slow, which limits their usefulness. In this paper we describe an optimal algorithm which computes all depth contours in &Ogr;(n 2) time …