## Estimating the number of clusters in a data set via the gap statistic.(English)Zbl 0979.62046

Summary: We propose a method (the ‘gap statistic’) for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g., $$K$$-means or hierarchical), comparing the change in within-cluster dispersion with that expected under an appropriate reference null distribution. Some theory is developed for the proposal and a simulation study shows that the gap statistic usually outperforms other methods that have been proposed in the literature.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects)

### Keywords:

hierarchy; K-means; uniform distribution; groups; clustering
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