Stability of $K$-Means Clustering

@inproceedings{Rakhlin2006StabilityO,
  title={Stability of \$K\$-Means Clustering},
  author={Alexander Rakhlin and Andrea Caponnetto},
  booktitle={NIPS},
  year={2006}
}
We phrase K-means clustering as an empirical risk minimization procedure over a class ℋK and explicitly calculate the covering number for this class. Next, we show that stability of K-means clustering is characterized by the geometry of ℋK with respect to the underlying distribution. We prove that in the case of a unique global minimizer, the clustering solution is stable with respect to complete changes of the data, while for the case of multiple minimizers, the change of Ω(n1/2) samples… CONTINUE READING

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