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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Dan Chen, Olivier Devillers, John Iacono, Stefan Langerman, Pat Morin. Oja centers and centers of gravity. Computational Geometry, Elsevier, 2013, 46 (2), pp.140-147. ⟨10.1016/j.comgeo.2012.04.004⟩. ⟨hal-00787177⟩

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