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Two Principal Points of Symmetric Distributions

  • Masahiro Mizuta
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In the present article, we discuss some conditions on the existence of asymmetric 2-principal points of univariate symmetric distributions and show some examples of 2-principal points that are asymmetric.

k-Principal points of a distribution, proposed by Flury(1990), mean k points that minimize the expected squared distance from the nearest of the point with respect to the distribution. The criterion of principal points is the almost same as that of k-means clustering. The k-means clustering is a method for a data set, but the concept of principal points is a theory for theoretical distributions.

Many people may guess that principal points of symmetric distributions are symmetric but Flury shows counter examples. We study conditions for symmetric or asymmetric principal points. A characteristic function p(c) for 2- principal points is defined in the paper. We investigate 2-principal points of mixed normal distributions with the characteristic function.

Keywords

Cluster Analysis k-means Optimal Allocation 

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Masahiro Mizuta
    • 1
  1. 1.Division of Systems and Information EngineeringHokkaido UniversityJapan

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