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The Ward linkage method in agglomerative hierarchical clustering computes the distance between two clusters using the within-group variance, which results in a weighted squared distance between cluster centers. Therefore, Ward linkage method doesn't rely on the distances of single elements, so it should be independent on the metric (euclidean , manhattan, squared euclidean...) used to compute the distance among the elements, because in the end the linkage criterion is based on the variance of the clusters which has a definite formula independently from the chosen metric. Nonetheless if I try the hclust function in R I obtain different results depending on the distance metric among the elements. Why?

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# Hierarchical Clustering: Ward linkage

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