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Why Ellipsoid Constraints, Ellipsoid Clusters, and Riemannian Space-Time: Dvoretzky’s Theorem Revisited

  • Karen VillaverdeEmail author
  • Olga Kosheleva
  • Martine Ceberio
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 539)

Abstract

In many practical applications, we encounter ellipsoid constraints, ellipsoid-shaped clusters, etc. A usual justification for this ellipsoid shape comes from the fact that many real-life quantities are normally distributed, and for a multi-variate normal distribution, a natural confidence set (containing the vast majority of the objects) is an ellipsoid. However, ellipsoids appear more frequently than normal distributions (which occur in about half of the cases). In this paper, we provide a new justification for ellipsoids based on a known mathematical result – Dvoretzky’s Theorem.

Keywords

ellipsoids constraints clusters tensors space-time physics Dvoretzky’s theorem 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Karen Villaverde
    • 1
    Email author
  • Olga Kosheleva
    • 2
  • Martine Ceberio
    • 2
  1. 1.Department of Computer ScienceNew Mexico State UniversityLas CrucesUSA
  2. 2.University of Texas at El PasoEl PasoUSA

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