Applying genetic algorithms to search for the best hierarchical clustering of a dataset

Abstract We apply genetic algorithms to get the optimal, in a least squares sense, hierarchical clustering of a dataset. We base this on the bijection between the set of hierarchical classifications of a dataset and the set of ultrametric distances. This bijection makes it possible to measure how good a hierarchical classification is, by calculating the L 2 norm between the ultrametric distance matrix associated with the hierarchical classification and the proximity matrix of the dataset. Our results are shown to improve on other methods which have been proposed, based on the ultrametric.

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