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From Wikipedia, the free encyclopedia
In statistics, and especially in biostatistics, cophenetic correlation[1] (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points. Although it has been most widely applied in the field of biostatistics (typically to assess cluster-based models of DNA sequences, or other taxonomic models), it can also be used in other fields of inquiry where raw data tend to occur in clumps, or clusters.[2] This coefficient has also been proposed for use as a test for nested clusters.[3]
Suppose that the original data {Xi} have been modeled using a cluster method to produce a dendrogram {Ti}; that is, a simplified model in which data that are "close" have been grouped into a hierarchical tree. Define the following distance measures.
Then, letting be the average of the x(i, j), and letting be the average of the t(i, j), the cophenetic correlation coefficient c is given by[4]
It is possible to calculate the cophenetic correlation in R using the dendextend R package.[5]
In Python, the SciPy package also has an implementation.[6]
In MATLAB, the Statistic and Machine Learning toolbox contains an implementation.[7]
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