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