A minor variant of Hartigan's k-means algorithm delivers 2-5% better clustering performance than the original, with gains increasing in high dimensions or large k.
Jain, Data clustering: 50 years beyond K-means, Pattern Recognition Letters 31 (2010), p
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An effective variant of the Hartigan $k$-means algorithm
A minor variant of Hartigan's k-means algorithm delivers 2-5% better clustering performance than the original, with gains increasing in high dimensions or large k.