TY - JOUR
T1 - Definition and properties ofm-dimensional n-principal points
AU - Matsuura, Shun
AU - Kurata, Hiroshi
PY - 2013/1/11
Y1 - 2013/1/11
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
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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 -