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.
Publié le : 1981-01-14
Classification:
Clustering criterion,
minimising within cluster sum of squares,
$k$-means,
strong consistency,
uniform strong law of large numbers,
62H30,
60F15
@article{1176345339,
author = {Pollard, David},
title = {Strong Consistency of $K$-Means Clustering},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 135-140},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345339}
}
Pollard, David. Strong Consistency of $K$-Means Clustering. Ann. Statist., Tome 9 (1981) no. 1, pp. 135-140. http://gdmltest.u-ga.fr/item/1176345339/