How to calculate the cophenetic similarity between two individual in two dendograms or between two clustering methods?

Question

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.

Answer 1

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)