Figure 1.

The two panels illustrate the cluster properties of size, shape, and orientation using simple hypothetical examples of two clusters that are distinguished on two clustering variables. The two clustering variables intersect at their mean values; therefore, one cluster has low scores on both clustering variables while the other cluster has high scores on both. Panel A depicts the scenario of two clusters that differ in size or volume but have the same shape, specifically, a spherical shape. The spherical shape is due to the two clustering variables being uncorrelated within each cluster. Panel B depicts the scenario of two clusters that differ in size and orientation, but have the same shape. Because a correlation is present between the clustering variables within each cluster (negative correlation within the larger cluster, positive correlation within the smaller cluster), these clusters have an elliptical shape and the property of orientation (not present for spherical clusters).