The Fowlkes–Mallows Statistic and the Comparison of Two Independently Determined Dendrograms

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Abstract
When interpreting the results of a cluster analysis, it is important to understand why specific clustering patterns arise. Comparison of a "dependent" dendrogram with a second, independently determined "covariate" dendrogram (i.e. one that is based solely on information provided by various explanatory variables) is a simple way of investigating the role played by the covariates. The Fowlkes–Mallows statistic, which is a measure of the degree of similarity between two dendrograms, can be used to test the null hypothesis that two dendrograms are unrelated. We show that the Fowlkes–Mallows test can be usefully employed in the systematic comparison of a dependent dendrogram and covariate dendrogram. Since the test is nonparametric, it is applicable to a wide range of problems. As an illustrative example, a species abundance matrix for several benthic communities is subjected to a standard cluster analysis, and the resultant (dependent) dendrogram is compared with a clustering based on the geographic location of the communities. At least some of the clustering seen in the dependent dendrogram can be attributed to the geographic proximity of the stations.

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