Principal points

Abstract

The k principal points of a p -variate random variable X are defined as those points ξ l ,…ξ k which minimize the expected squared distance of X from the nearest of the ξ j . This paper presents results on the principal points of univariate symmetric distributions, the univariate and bivariate normal distribution, multivariate elliptical distributions, and multivariate distributions in general. In the cases of normal and elliptical distributions, the relationship between principal points and principal components is studied.