pheatmap: manually re-order leaves in dendogram

I have created a heatmap with a corresponding dendogram based on hierarchical clustering with {pheatmap}. I would like to change the order of the leaves in the dendogram, manually, based on what I see visually.

First, can anyone confirm that this is statistically correct and allowed? (in theory that should not change the between-cluster distance, but maybe I am wrong).

Second, any suggestions on how to change the order of the leaves would be appreciated!

A reproductible example with the iris data:

data(iris)
pheatmap(iris[1:4], cutree_cols = 3)

For your example you can use a callback function to reorder the columns, e.g.

library(pheatmap)
data(iris)
colnames(iris)
#> [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"

callback = function(hc, mat){
  sv = svd(t(mat))$v[,c(1)]
  dend = reorder(as.dendrogram(hc), wts = sv^2)
  as.hclust(dend)
}

#svd(t(iris[c(4, 2, 3, 1)]))$v[,1]

pheatmap(iris[c(4, 2, 3, 1)], cutree_cols = 3, clustering_callback = callback)

^{Created on 2022-09-28 by the reprex package (v2.0.1)}

For your actual data, you will probably need to fiddle around with the weights to get the columns in your desired order, e.g.

library(pheatmap)
data(iris)
colnames(iris)
#> [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width"  "Species"

callback = function(hc, mat){
  sv = svd(t(mat))$v[,c(2)]
  dend = reorder(as.dendrogram(hc), wts = sv)
  as.hclust(dend)
}

#svd(t(iris[c(4, 2, 3, 1)]))$v[,2]

pheatmap(iris[c(4, 2, 3, 1)], cutree_cols = 3, clustering_callback = callback)

^{Created on 2022-09-28 by the reprex package (v2.0.1)}

This feature is described briefly at the end of the help file:

?pheatmap
...

# Modify ordering of the clusters using clustering callback option
callback = function(hc, mat){
    sv = svd(t(mat))$v[,1]
    dend = reorder(as.dendrogram(hc), wts = sv)
    as.hclust(dend)
}

pheatmap(test, clustering_callback = callback)

## Not run: 
# Same using dendsort package
library(dendsort)

callback = function(hc, ...){dendsort(hc)}
pheatmap(test, clustering_callback = callback)

## End(Not run)