### Abstract

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 language | English |
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Pages (from-to) | 267-282 |

Number of pages | 16 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 42 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 Jan 11 |

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability

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## Cite this

Matsuura, S., & Kurata, H. (2013). Definition and properties ofm-dimensional n-principal points.

*Communications in Statistics - Theory and Methods*,*42*(2), 267-282. https://doi.org/10.1080/03610926.2011.581791