Strong Consistency of $K$-Means Clustering

David Pollard

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.

Keywords

MathematicsCluster analysisConsistency (knowledge bases)StatisticsStrong consistencySample (material)Convergence (economics)Cluster (spacecraft)CombinatoricsEconometricsDiscrete mathematicsComputer science

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Publication Info

Year: 1981
Type: article
Volume: 9
Issue: 1
Citations: 452
Access: Closed

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APA Style

                            
                                    David Pollard
                                
                            (1981). 
                            Strong Consistency of $K$-Means Clustering. 
                            The Annals of Statistics
                            , 9
                            (1)
                            .
                            https://doi.org/10.1214/aos/1176345339

Identifiers

DOI: 10.1214/aos/1176345339