Oja centers and centers of gravity

Authors:
Dan Chen;Olivier Devillers;John Iacono;Stefan Langerman;Pat Morin
Affiliations:
School of Computer Science, Carleton University, Canada;INRIA Sophia Antipolis - Méditerranée, France;Department of Computer and Information Science, Polytechnic University, United States;Département dInformatique, Université Libre de Bruxelles, Belgium;School of Computer Science, Carleton University, Canada
Venue:
Computational Geometry: Theory and Applications
Year:
2013

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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.