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A parametric k-means algorithm

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wright State University, Dayton, OH, USA

    Thaddeus Tarpey

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  1. Thaddeus Tarpey
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Correspondence to Thaddeus Tarpey.

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Tarpey, T. A parametric k-means algorithm. Computational Statistics 22, 71–89 (2007). https://doi.org/10.1007/s00180-007-0022-7

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