Computes the cophenetic distances for a hierarchical clustering.
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an R object representing a hierarchical clustering.
For the default method, an object of class
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
that all leaves of the dendrogram object have non-null labels.
An object of class
Sneath, P.H.A. and Sokal, R.R. (1973) Numerical Taxonomy: The Principles and Practice of Numerical Classification, p. 278 ff; Freeman, San Francisco.
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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
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