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I am doing clustering of variables using hclustvar() function from ClustOfVar package in R. The example given in R for the decathlon data is:

data(decathlon)

tree <- hclustvar(X.quanti=decathlon[,1:10], init=NULL)

plot(tree)

The function does the PCA and then analyze projections of variables on main components to detect those variables that have similar coordinates. However I still don't know how to interprete the Y-axis on the plot which is called Height. Could anybody help me with the interpretation? Thanks!

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As stated on the package documentation – p.9, hclustvar() provides ascendant hierarchical clustering of a set of variables. In order to do this hierarchical clustering, it should compute a distance metric between variables and clusters. In the case of hclustvar(), this distance is based on correlation between variables and then between clusters – i.e group of variables (cf. the aggregation criterion defined in the package documentation. For more information, look at the paper dedicated to the package on jstatsoft. Paper title: ClustOfVar: An R Package for the Clustering of Variables).

The Y-axis (Height) is the value of this distance metric. If you see two clusters merged at a height x, it means that the distance between those clusters is x. Here for example, the minimal height is 0.3842319 and this is the distance between Shop.put and Discus which are the closest variables. This distance is equal to 1 - cor(decathlon$Shot.put, decathlon$Discus). Note that length(tree$height) == n-1, with n being the number of variables, since you need at least two variables to generate the first cluster.

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  • $\begingroup$ Seems not mention how it is involved with PCA $\endgroup$ Jun 9, 2023 at 6:41

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