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Measuring centrality and dispersion in directional datasets: the ellipsoidal cone covering approach

Author

Listed:
  • Alberto Seeger

    (Université d’Avignon)

  • José Vidal -Nuñez

    (Universidad de Alicante)

Abstract

Consider a finite collection $$\{\xi _k\}_{k=1}^p$$ { ξ k } k = 1 p of vectors in the space $$\mathbb {R}^n$$ R n . The $$\xi _k$$ ξ k ’s are not to be seen as position points but as directions. This work addresses the problem of computing the ellipsoidal cone of minimal volume that contains all the $$\xi _k$$ ξ k ’s. The volume of an ellipsoidal cone is defined as the usual n-dimensional volume of a certain truncation of the cone. The central axis of the ellipsoidal cone of minimal volume serves to define the central direction of the datapoints, whereas its volume can be used as measure of dispersion of the datapoints.

Suggested Citation

  • Alberto Seeger & José Vidal -Nuñez, 2017. "Measuring centrality and dispersion in directional datasets: the ellipsoidal cone covering approach," Journal of Global Optimization, Springer, vol. 68(2), pages 279-306, June.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:2:d:10.1007_s10898-016-0464-y
    DOI: 10.1007/s10898-016-0464-y
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    References listed on IDEAS

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    1. Annabella Astorino & Manlio Gaudioso & Alberto Seeger, 2014. "An illumination problem: optimal apex and optimal orientation for a cone of light," Journal of Global Optimization, Springer, vol. 58(4), pages 729-750, April.
    2. J. L. Goffin, 1980. "The Relaxation Method for Solving Systems of Linear Inequalities," Mathematics of Operations Research, INFORMS, vol. 5(3), pages 388-414, August.
    3. Peng Sun & Robert M. Freund, 2004. "Computation of Minimum-Volume Covering Ellipsoids," Operations Research, INFORMS, vol. 52(5), pages 690-706, October.
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