### 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 |

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### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability

### Cite this

*Communications in Statistics - Theory and Methods*,

*42*(2), 267-282. https://doi.org/10.1080/03610926.2011.581791

**Definition and properties ofm-dimensional n-principal points.** / Matsuura, Shun; Kurata, Hiroshi.

Research output: Contribution to journal › Article

*Communications in Statistics - Theory and Methods*, vol. 42, no. 2, pp. 267-282. https://doi.org/10.1080/03610926.2011.581791

}

TY - JOUR

T1 - Definition and properties ofm-dimensional n-principal points

AU - Matsuura, Shun

AU - Kurata, Hiroshi

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Elliptically symmetric distribution

KW - Location mixture

KW - Mean squared distance

KW - Principal points

KW - Spherically symmetric distribution

UR - http://www.scopus.com/inward/record.url?scp=84872018191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872018191&partnerID=8YFLogxK

U2 - 10.1080/03610926.2011.581791

DO - 10.1080/03610926.2011.581791

M3 - Article

AN - SCOPUS:84872018191

VL - 42

SP - 267

EP - 282

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

SN - 0361-0926

IS - 2

ER -