Some remarks on the R2 for clustering

A common descriptive statistic in cluster analysis is the R-2 that measures the overall proportion of variance explained by the cluster means. This note highlights properties of the R-2 for clustering. In particular, we show that generally the R-2 can be artificially inflated by linearly transforming the data by stretching and by projecting. Also, the R-2 for clustering will often be a poor measure of clustering quality in high-dimensional settings. We also investigate the R-2 for clustering for misspecified models. Several simulation illustrations are provided highlighting weaknesses in the clustering R-2, especially in high-dimensional settings. A functional data example is given showing how that R-2 for clustering can vary dramatically depending on how the curves are estimated.