Solved – Cophenetic distance matrix to a dendrogram

dendrogramhierarchical clusteringr

In hierarchical clustering procedure, a distance matrix is used to construct a dendrogram with an appropriate method of clustering. In the process of constructing a dendrogram, a cophenetic matrix is computed. I understand that such a cophenetic matrix is used to assess clustering consistency.

How can I use a cophenetic matrix as such to plot the dendrogram?

Best Answer

You can just recreate the plot using hclust on the cophenetic of the object, and it would get you what you want (the method used in hclust doesn't matter).

set.seed(2015-04-26)
dat <- (matrix(rnorm(100), 4, 24))
dat_dist <- dist(dat)
hc1 <- hclust(dat_dist)

dat_dist

hc2 <- hclust(cophenetic(hc1), method = "complete")
hc3 <- hclust(cophenetic(hc1), method = "single")
hc4 <- hclust(cophenetic(hc1), method = "ave")

par(mfrow = c(1,4))
plot(hc1)
plot(hc2)
plot(hc3)
plot(hc4)

enter image description here

Related Solutions

Solved – How to convert a dendrogram back into a distance matrix

You can try to have a look at cophenetic distance. According to the R help page: "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. Note that this distance has many ties and restrictions. It can be argued that a dendrogram is an appropriate summary of some data if the correlation between the original distances and the cophenetic distances is high. Otherwise, it should simply be viewed as the description of the output of the clustering algorithm. "

d1 <- dist(USArrests)
hc <- hclust(d1, "ave")
d2 <- cophenetic(hc)
cor(d1, d2) # 0.7659

Solved – Validate dendrogram in cluster analysis: What is the meaning of cophenetic correlation coefficient

The cophenetic correlation coefficient is defined as the linear correlation between the dissimilarities $d_{ij}$ between each pair of observations $(i,j)$ and their corresponding cophenetic distances $d_{ij}^{coph}$, which is the intergroup dissimilarity at which the observations $i, j$ first merged together in the same cluster.

So you get the cophenetic correlation coefficient $CCC$ by calculating the correlation between those values. Let $D$ be the distance matrix according to $d$ and $Z$ be the distance matrix according to $d^{coph}$, $\bar{D}, \bar{Z}$ denotes the means of $d_{ij}$ and $d_{ij}^{coph}$ respectively, then

$CCC(D,Z) = Cor(D,Z) = \frac{\sum\limits_{i<j} (D_{ij} - \bar{D})(Z_{ij} - \bar{Z}) }{\sqrt{\sum\limits_{i<j} (D_{ij} - \bar{D})^2 \sum\limits_{i<j} (Z_{ij} - \bar{Z})^2 }}$

(see: Mathworks Documentation: cophenetic correlation coefficient)

This should be equal to what you have done by calculating

cor(euclidian_dist, coph)

So, I think your assumption is correct.

Best Answer

Related Solutions

Solved – How to convert a dendrogram back into a distance matrix

Solved – Validate dendrogram in cluster analysis: What is the meaning of cophenetic correlation coefficient

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