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January, 1981 Strong Consistency of $K$-Means Clustering
David Pollard
Ann. Statist. 9(1): 135-140 (January, 1981). DOI: 10.1214/aos/1176345339

Abstract

A random sample is divided into the $k$ clusters that minimise the within cluster sum of squares. Conditions are found that ensure the almost sure convergence, as the sample size increases, of the set of means of the $k$ clusters. The result is proved for a more general clustering criterion.

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David Pollard. "Strong Consistency of $K$-Means Clustering." Ann. Statist. 9 (1) 135 - 140, January, 1981. https://doi.org/10.1214/aos/1176345339

Information

Published: January, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0451.62048
MathSciNet: MR600539
Digital Object Identifier: 10.1214/aos/1176345339

Subjects:
Primary: 62H30
Secondary: 60F15

Keywords: $k$-means , Clustering criterion , minimising within cluster sum of squares , strong consistency , uniform strong law of large numbers

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 1 • January, 1981
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