Strong Consistency of $K$-Means Clustering
Copyright policy )Strong Consistency of $K$-Means Clustering
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.
Strong limit theorems, Classification and discrimination; cluster analysis (statistical aspects), k-means clustering, clustering criterion, Clustering criterion, 60F15, strong consistency, uniform strong law of large numbers, almost sure convergence, minimising within cluster sum of squares, 62H30, $k$-means
Strong limit theorems, Classification and discrimination; cluster analysis (statistical aspects), k-means clustering, clustering criterion, Clustering criterion, 60F15, strong consistency, uniform strong law of large numbers, almost sure convergence, minimising within cluster sum of squares, 62H30, $k$-means
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