#### Title

A Parametric K-Means Algorithm

#### Document Type

Article

#### Publication Date

2007

#### Abstract

The k points that optimally represent a distribution (usually in terms of a squared error loss) are called the k principal points. This paper presents a computationally intensive method that automatically determines the principal points of a parametric distribution. Cluster means from the k-means algorithm are nonparametric estimators of principal points. A parametric k-means approach is introduced for estimating principal points by running the k-means algorithm on a very large simulated data set from a distribution whose parameters are estimated using maximum likelihood. Theoretical and simulation results are presented comparing the parametric k-means algorithm to the usual k-means algorithm and an example on determining sizes of gas masks is used to illustrate the parametric k-means algorithm.

#### Repository Citation

Tarpey, T.
(2007). A Parametric K-Means Algorithm. *Computational Statistics, 22* (1), 71-89.

https://corescholar.libraries.wright.edu/math/180

#### DOI

10.1007/s00180-007-0022-7