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Oja medians and centers of gravity.

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TLDR
Oja’s original definition, the sum is normalized by dividing by (|S| d ) .
Abstract
The bound in (1) is not known to be tight. The bound in (2) is tight, up to a lower-order term, for some point sets S. ∗This work was initiated during the Workshop on Computational Geometry 2006 in Caldes de Malavella. The authors wish to thank Ferran Hurtado and the organizers for the opportunity of working on this topic. †School of Computer Science, Carleton University, dchen4@connect.carleton.ca, morin@scs.carleton.ca ‡INRIA Sophia Antipolis Méditerranée, France. Olivier.Devillers@sophia.inria.fr §Department of Computer and Information Science, Polytechnic University, jiacono@poly.edu ¶Département d’Informatique, Université Libre de Bruxelles, stefan.langerman@ulb.ac.be 1In Oja’s original definition, the sum is normalized by dividing by (|S| d ) . We omit this here since it changes none of our results and clutters our formulas. 1.2 Related Results

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Lectures on Discrete Geometry

Jiri Matousek
TL;DR: This book is primarily a textbook introduction to various areas of discrete geometry, in which several key results and methods are explained, in an accessible and concrete manner, in each area.
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On a Notion of Data Depth Based on Random Simplices

Regina Y. Liu
- 01 Mar 1990 - 
TL;DR: In this article, the simplical depth of a point is defined as the probability that the point is contained inside a random simplex whose vertices are $p + 1$ independent observations from the distribution of the point.
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Combinatorial Geometry

János Pach, +1 more
TL;DR: This discipline emerged from number theory after the fruitful observation made by Minkowski (1896) that many important results in diophantine approximation (and in some other central fields of number theory) can be established by easy geometric arguments.
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Descriptive Statistics for Multivariate Distributions

TL;DR: In this paper, the concepts location, scatter, skewness and kurtosis of multivariate distributions are studied and measures of these properties are introduced which include some new generalizations of well-known univariate statistics.