Oja centers and centers of gravity

Dan Chen; Olivier Devillers; John Iacono; Stefan Langerman; Pat Morin

doi:10.1016/j.comgeo.2012.04.004

Oja centers and centers of gravity

Dan Chen, Olivier Devillers, John Iacono, Stefan Langerman, Pat Morin

Research output: Contribution to journal › Article › peer-review

Abstract

Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.

Original language	English (US)
Pages (from-to)	140-147
Number of pages	8
Journal	Computational Geometry: Theory and Applications
Volume	46
Issue number	2
DOIs	https://doi.org/10.1016/j.comgeo.2012.04.004
State	Published - Feb 2013

Keywords

Centerpoint theorem
Data depth
Oja depth

ASJC Scopus subject areas

Computer Science Applications
Geometry and Topology
Control and Optimization
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.comgeo.2012.04.004

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title = "Oja centers and centers of gravity",

abstract = "Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.",

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author = "Dan Chen and Olivier Devillers and John Iacono and Stefan Langerman and Pat Morin",

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T1 - Oja centers and centers of gravity

AU - Chen, Dan

AU - Devillers, Olivier

AU - Iacono, John

AU - Langerman, Stefan

AU - Morin, Pat

PY - 2013/2

Y1 - 2013/2

N2 - Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.

AB - Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.

KW - Centerpoint theorem

KW - Data depth

KW - Oja depth

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JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

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ER -

Oja centers and centers of gravity

Abstract

Keywords

ASJC Scopus subject areas

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