Approximate computation of projection depths - Kölner UniversitätsPublikationsServer

Dyckerhoff, Rainer ORCID: 0000-0002-3631-8497, Mozharovskyi, Pavlo ORCID: 0000-0002-1925-3337 and Nagy, Stanislav ORCID: 0000-0002-8610-4227 (2021). Approximate computation of projection depths. Comput. Stat. Data Anal., 157. AMSTERDAM: ELSEVIER. ISSN 1872-7352

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DOI:10.1016/j.csda.2020.107166

Abstract

Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in R-d. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional projections of the data, then the depth satisfies the so-called projection property. Such depths form an important class that includes many of the depths that have been proposed in literature. For depths that satisfy the projection property an approximate algorithm can easily be constructed since taking the minimum of the depths with respect to only a finite number of one-dimensional projections yields an upper bound for the depth with respect to the multivariate data. Such an algorithm is particularly useful if no exact algorithm exists or if the exact algorithm has a high computational complexity, as is the case with the halfspace depth or the projection depth. To compute these depths in high dimensions, the use of an approximate algorithm with better complexity is surely preferable. Instead of focusing on a single method we provide a comprehensive and fair comparison of several methods, both already described in the literature and original. (C) 2021 Elsevier B.V. All rights reserved.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Dyckerhoff, Rainer	UNSPECIFIED	orcid.org/0000-0002-3631-8497	UNSPECIFIED
Mozharovskyi, Pavlo	UNSPECIFIED	orcid.org/0000-0002-1925-3337	UNSPECIFIED
Nagy, Stanislav	UNSPECIFIED	orcid.org/0000-0002-8610-4227	UNSPECIFIED