TY - JOUR

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

AU - Matsuura, Shun

AU - Kurata, Hiroshi

N1 - Funding Information:
The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which led to significant improvements in this article. Kurata’s portion of this work was supported by JSPS KAKENHI Grant Number 23700341. Kurata’s portion of this work was supported by JSPS KAKENHI Grant Number 20243016, 21500272.

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 -