Definition and properties ofm-dimensional n-principal points

Shun Matsuura, Hiroshi Kurata

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


In this article, we introduce the notion of "m-dimensional n-principal points," which is a generalization of the notion of n-principal points. A set of m-dimensional n-principal points of a distribution is defined as a set of n points that optimally represents the distribution in terms of mean squared distance subject to the condition that the dimension of the linear subspace spanned by the n points is at most m. Its properties and connections to principal components are investigated for elliptically symmetric distributions and a location mixture of spherically symmetric distributions.

Original languageEnglish
Pages (from-to)267-282
Number of pages16
JournalCommunications in Statistics - Theory and Methods
Issue number2
Publication statusPublished - 2013


  • Elliptically symmetric distribution
  • Location mixture
  • Mean squared distance
  • Principal points
  • Spherically symmetric distribution

ASJC Scopus subject areas

  • Statistics and Probability


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