New upper bounds on the quality of the PCA bounding boxes in r2 and r3

  • Authors:

  • Darko Dimitrov;Christian Knauer;Klaus Kriegel;G. Rote

  • Affiliations:

  • Institut f, D-14195 Berlin, Germany;Institut f, D-14195 Berlin, Germany;Institut f, D-14195 Berlin, Germany;Institut f, D-14195 Berlin, Germany

  • Venue:
  • SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
  • Year:
  • 2007

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Abstract

Principal component analysis (PCA) is commonly used to compute a bounding box of a point set in Rd. The popularity of this heuristic lies in its speed, easy implementation and in the fact that usually, PCA bounding boxes quite well approximate the minimum-volume bounding boxes.Since there are examples of discrete points sets in the plane, showing that the worst case ratio of the volume ofthe PCA bounding box and the volume of the minimum-volume bounding box tends to infinity,we consider PCA bounding boxes for continuous sets, especially for the convex hull of a point set. Here, we contributenew upper bounds on the approximation factor of PCA bounding boxesof convex sets in R2 and R3.