Mathematica 10.4 includes new functions for dendrograms. So far I found Dendrogram and ClusteringTree. Both take unclustered data as input and output a visualization.

But is there a way to obtain a symbolic representation of a dendrogram, i.e. to separate the clustering and the visualization steps? This would be useful in many cases, such as

• producing the dendrogram data in another way and plotting it with Mathematica,
• or doing manipulations on the dendrogram data, such as truncating it for clearer visualization
• or using a completely different visualization function to plot dendrogram data computed with Mathematica. For example, one might want to highlight the clusters in colour given some cutoff. Or plot a radial dendrogram instead.

MATLAB works like this: it has the computation and visualization steps separated, and it has a representation for dendrograms that can be used for computation (not only visualization). http://www.mathworks.com/help/stats/dendrogram.html Then people can easily extend its dendrogram functionality.

The old HierarchicalClustering Mathematica package also separates these two steps: it has DirectAgglomerate and DendrogramPlot. But that package is outdated in many other ways and was long due for an update.

Note that the output of ClusteringTree is a Graph (not just graphics), but that is not suitable as such a representation because it does not include the dissimilarity values. Nor can it be directly plotted as a dendrogram.