The Annals of Statistics

Strong Consistency of $K$-Means Clustering

David Pollard

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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.

Article information

Source
Ann. Statist., Volume 9, Number 1 (1981), 135-140.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345339

Digital Object Identifier
doi:10.1214/aos/1176345339

Mathematical Reviews number (MathSciNet)
MR600539

Zentralblatt MATH identifier
0451.62048

JSTOR
links.jstor.org

Subjects
Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 60F15: Strong theorems

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

Citation

Pollard, David. Strong Consistency of $K$-Means Clustering. Ann. Statist. 9 (1981), no. 1, 135--140. doi:10.1214/aos/1176345339. https://projecteuclid.org/euclid.aos/1176345339


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