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Assume we have a dendogram (hierarchical clusterisation tree), can we define a data partitioning in K clusters, by cutting the branches of the tree at some levels in the tree below the root node?

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Yes absolutely, in fact that's exactly how one obtains actual clusters with hierarchical clustering.

With hierarchical clustering it's possible to decide the number of clusters (i.e. the level of "precision") after obtaining the tree (dendogram).

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