Oja centers and centers of gravity

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

    Research output: Contribution to journalArticle

    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 languageEnglish (US)
    Pages (from-to)140-147
    Number of pages8
    JournalComputational Geometry: Theory and Applications
    Volume46
    Issue number2
    DOIs
    StatePublished - Feb 1 2013

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    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

    Cite this

    Chen, D., Devillers, O., Iacono, J., Langerman, S., & Morin, P. (2013). Oja centers and centers of gravity. Computational Geometry: Theory and Applications, 46(2), 140-147. https://doi.org/10.1016/j.comgeo.2012.04.004