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I use Aitchison distance as the input to a hierarchical clustering dendrogram. I started labeling and interpreting the dendrogram but wasn't sure about a few aspects:

  • Are the vertical distances on the dendrogram in the same units as the input dendrogram? For example, if I label the y-axis as "Aitchison Distance" is that accurate?

  • When calculating branch distance, is that in units of the original distance matrix? (e.g., calculated w/ http://etetoolkit.org/docs/latest/tutorial/tutorial_trees.html#working-with-branch-distances)

  • In regards to the question above, is branch distance usually interpreted the same as "shortest path" in a graph?

O.rka
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  • [This](https://stats.stackexchange.com/q/195446/3277) answers your points, but you read through attentively. Colligation coefficients are _based_ on the input distances. For some linkage methods, they _are_ the values from the matrix. The shortest path paradigm is related to the nearest neighbour method, not to all linkage methods. – ttnphns Feb 20 '22 at 18:52
  • Thank you. I'm trying to distill down the info from the linked out post. I have a few follow up questions: 1) Which of the linkage methods produce dendrograms whose y-axis distances are in the same units as the original distance matrix?; 2) what would be the most appropriate y-label for all hierarchical clustering dendrograms?; 3) In the case of something like ward linkage, would the y-label be "ward linkage of aitchison distance"?. All of this is assuming a horizontal dendrogram. – O.rka Feb 23 '22 at 20:15
  • Actually, the questions you are asking now are uncovered in the linked answer. It is said there how exactly the between-cluster disrance is computed. So one can deduce easily which methods give colligation coefs. on the same scale as the input ones. – ttnphns Feb 23 '22 at 20:45

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