Cophenetic Distances for a Hierarchical Clustering

Computes the cophenetic distances for a hierarchical clustering.

multivariate, cluster
cophenetic(x) "cophenetic"(x) "cophenetic"(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" in package \href{}{\pkg{#1}}clustercluster.

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".


Sneath, P.H.A. and Sokal, R.R. (1973) Numerical Taxonomy: The Principles and Practice of Numerical Classification, p.\ifelse{latex}{\out{~}}{ } 278 ff; Freeman, San Francisco.

See Also

dist, hclust

  • cophenetic
  • cophenetic.default
  • cophenetic.dendrogram
library(stats) require(graphics) 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] d0 utils::str(upgma <- hclust(d0, method = "average")) plot(upgma, hang = -1) # (d.coph <- cophenetic(upgma)) cor(d0, d.coph) # 0.9911
Documentation reproduced from package stats, version 3.2.5, License: Part of R 3.2.5

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