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How can I calculate the cophenetic distance for an individual within two trees (not between two whole trees)?

I want to calculate the similarity/dissimilarity in position per individual within two dendrograms and show the result in the row color of a combined heatmap and dendrogram using R packages dendextend and heatmaply.

Grant Miller
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Niels Zondervan
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  • cophenetic is the distance between two items (leaves) in a dendrogram (tree). You can see that matrix of distances of a dendrogram using the cophenetic function. Is that what you are looking for? (if not, I suspect your question may needs some more clarification, and a simple example will also help :) ) – Tal Galili Sep 01 '18 at 21:54
  • Thx, basically that is what I need. I could only find examples that compare two whole trees, so an average of all cophenetic distances insteaad of single cophenetic distance. In my case I want to compare the correlate the cophenetic distance for all pairs of one leave to all others in a tree, so Tree1: A-B, A-C, A-D, A-E...A-n in one tree and correlate these with Tree2: A-B, A-C, A-D, A-E. This should give me a measure of similarity in position for one leave in two trees. Thx for helping me clarify. – Niels Zondervan Sep 03 '18 at 07:58

2 Answers2

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The cophenetic distance between two observations that have been clustered is defined to be the intergroup dissimilarity at which the two observations are first combined into a single cluster. Look here for a worked example.For an indepth discussion, I recommend this SO post. And here you can see the R implementation.

maverick
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Thanks all for the help, based on the links provided by vilisSO and the answer from Grant, I made the following code to calculate the correlation between cophenetic distance in two trees based on full data and a sub sample of the data. For each leave in the dendrogram, the correlation is calculated between the for the cophenetic distances vector in the two trees o: enter image description here

## Compare cophenetic similarity between leaves in two trees build on full data and subsample of the data

# 1 ) Generate random data to build trees
set.seed(2015-04-26)
dat <- (matrix(rnorm(100), 10, 50)) # Dataframe with 50 columns
datSubSample <- dat[, sample(ncol(dat), 30)] #Dataframe with 30 columns sampled from the dataframe with 50
dat_dist1 <- dist(datSubSample)
dat_dist2 <- dist(dat)
hc1 <- hclust(dat_dist1)
hc2 <- hclust(ddat_dist2)

# 2) Build two dendrograms, one based on all data, second based a sample of the data (30 out of 50 columns)
dendrogram1 <- as.dendrogram(hc1)
dendrogram2 <- as.dendrogram(hc2)

# 3) For each leave in a tree get cophenetic distance matrix, 
# each column represent distance of that leave to all others in the same tree
cophDistanceMatrix1 <- as.data.frame(as.matrix(cophenetic(dendrogram1)))
cophDistanceMatrix2 <- as.data.frame(as.matrix(cophenetic(dendrogram2)))

# 4) Calculate correlation between cophenetic distance of a leave to all other leaves, between two trees
corPerLeave <- NULL # Vector to store correlations for each leave in two trees
for (leave in colnames(cophDistanceMatrix1)){
  cor <- cor(cophDistanceMatrix2[leave],cophDistanceMatrix1[leave])
  corPerLeave <- c(corPerLeave, unname(cor))
}

# 5) Convert cophenetic correlation to color to show in side bar of a heatmap
corPerLeave <-corPerLeave/max(corPerLeave) #Scale 0 to 1 correlation
byPal <- colorRampPalette(c('yellow','blue')) #blue yellow color palette, low correlatio = yellow
colCopheneticCor <- byPal(20)[as.numeric(cut(corPerLeave, breaks =20))]

# 6) Plot heatmap with dendrogram with side bar that shows cophenetic correlation for each leave 
row_dend  <- dendrogram2[enter image description here][1]
x  <- as.matrix(dat_dist)
heatmaply(x,colD = row_dend,row_side_colors=colCopheneticCor)
Niels Zondervan
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