cophenetic {stats}R Documentation

Cophenetic Distances for a Hierarchical Clustering


Computes the cophenetic distances for a hierarchical clustering.


## Default S3 method:
## S3 method for class 'dendrogram':


x an R object representing a hierarchical clustering. For the default method, an object of class hclust or with a method for as.hclust() such as agnes.


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.

cophenetic is a generic function. Support for classes which represent hierarchical clusterings (total indexed hierarchies) can be added by providing an as.hclust() or, more directly, a cophenetic() method for such a class.

The method for objects of class "dendrogram" requires that all leaves of the dendrogram object have non-null labels.


An object of class dist.


Robert Gentleman


Sneath, P.H.A. and Sokal, R.R. (1973) Numerical Taxonomy: The Principles and Practice of Numerical Classification, p. 278 ff; Freeman, San Francisco.

See Also

dist, hclust


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

## Example from Sneath & Sokal, Fig. 5-29, p.279
d0 <- c(1,3.8,4.4,5.1, 4,4.2,5, 2.6,5.3, 5.4)
attributes(d0) <- list(Size = 5, diag=TRUE)
class(d0) <- "dist"
names(d0) <- letters[1:5]
str(upgma <- hclust(d0, method = "average"))
plot(upgma, hang = -1)
(d.coph <- cophenetic(upgma))
cor(d0, d.coph) # 0.9911

[Package stats version 2.2.1 Index]