The Effects of Within-group Covariance Structure on Recovery in Cluster Analysis: I. The Bivariate Case

In a preliminary investigation, two Monte Carlo studies investigated the effects of within-group covariance structure on subgroup recovery by I0 hierarchical clustering methods. Data sets were 100 bivariate observations from two subgroups. Study 1 manipulated subgroup size, within-group correlation, within-group variance, and distance between centroids. Negative within-group correlation yielded much poorer recovery for all clustering methods. In addition, clustering method interacted with within-group variance. Study 2 manipulated subgroup size, within-group correlation, direction of the vector separating subgroup centroids, and distance between subgroup centroids. Superior recovery was associated with within-group correlation that matched the direction of subgroup separation. Results are interpreted according to the weakness of Euclidean distance as a measure of (dis)similarity.