Algorithms for bivariate zonoid depth
نویسندگان
چکیده
منابع مشابه
Algorithms for bivariate zonoid depth
Zonoid depth is a new notion of data depth proposed by Dy-ckerhoff et al [DKM96]. We give efficient algorithms for solving several zonoid depth problems for 2-dimensional (bi-variate) data. Data depth measures how deep or central a given point 0 in 1 3 2 is relative to a given data cloud or a probability distribution in 1 4 2. Some examples of data depth are halfspace, simplicial, convex hull p...
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The majority depth of a point with respect to a point set is the number of major sides it is in. An algorithm for majority depth in R is given in this paper, and it is the first algorithm to compute the majority depth. This algorithm runs in O((n+m) log n) time with Brodal and Jacob’s data structure, and in O ( (n + m) log n log log n ) time in the word RAM model.
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A randomized linear expected-time algorithm for computing the zonoid depth (Dyckerhoff et al 1996, Mosler 2002) of a point with respect to a fixed dimensional point set is presented.
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Under some mild conditions on probability distribution P , if limn Pn = P weakly then the sequence of zonoid depth functions with respect to Pn converges uniformly to the zonoid depth function with respect to P . © 2015 Elsevier Inc. All rights reserved.
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Simplicial depth is a way to measure how deep a point is among a set of points. EEcient algorithms to compute it are important to the usefulness of its applications, such as in multivariate analysis in statistics. A straightforward method takes O(n d+1) time when the points are in d-dimensional space. We discuss an algorithm that takes O(n 2) time when the points are in three-dimensional space,...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2008
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2007.05.007