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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 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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