Computing the Depth of a Flat (2001) [1 citations — 0 self]
Popular Tags
No tags have been applied to this document.
BibTeX | Add To MetaCart
author = {Marshall Bern and David Eppstein},
title = {Computing the Depth of a Flat},
booktitle = {Proc. 12th Symp. Discrete Algorithms},
year = {2001},
pages = {700--701}
}
Bookmarks
OpenURL
Abstract:
We compute the regression depth of a k-flat in a set of n points in R d , in time O(n d-2 + n log n) for 1 # k # d - 2. This contrasts with a bound of O(n d-1 + n log n) when k = 0or k = d - 1. 1 Introduction Regression depth was introduced by Hubert and Rousseeuw [7] as a distance-free quality measure for linear regression. The depth of a hyperplane is the minimum number of points crossed in any continuous motion taking the hyperplane to a vertical hyperplane (a "nonfit"). The deepest hyperplane provides a good fit even in the presence of skewed or data-dependent errors, and is robust against a constant fraction of arbitrary outliers. Due to its combinatorial nature, regression depth leads to many interesting geometric and algorithmic problems. A simple construction called the catline provides a line of depth #n/3# for n points in the plane [3]. The catline's depth bound is best possible, and more generally in R d the best depth bound is #n/(d + 1)# [1, 5]. On...
Citations
| 262 | Computational Geometry: An Introduction Through Randomized Algorithms – Mulmuley - 1994 |
| 37 | Computing location depth and regression depth in higher dimensions – Rousseeuw, Struyf - 1998 |
| 35 | Regression depth – ROUSSEEUW, HUBERT - 1999 |
| 10 | Regression depth and center points – Amenta, Bern, et al. - 2000 |
| 10 | The catline for deep regression – Hubert, Rousseeuw - 1998 |
| 9 | On depth and deep points: a calculus – Mizera - 1998 |
| 8 | Multivariate regression depth – BERN, EPPSTEIN |
| 3 | An O(n log n) algorithm for the hyperplane median – Langerman, Steiger - 2000 |
| 3 | Hyperplane depth and nested simplices – Steiger, Wenger - 1998 |
