Validating Cluster Analysis: Consistent Replication and Symmetry

Two simulation studies evaluated a cross-validation approach for cluster analyses (CA). Study 1 examined the extent to which the magnitude of replication and two aspects of replication, consistency and symmetry indicate recovery of true clusters for ten CA algorithms. Cluster size, number of clusters, covariance structure, number of variables, sample size, and error perturbation were systematically varied. Replication indices significantly predicted recovery. Study 2 evaluated replication as an indicator of the number of true clusters within a sample. Although on the average replication indices peak in the region of the true number of clusters, choosing the number of clusters by maximum replication results in a negatively biased estimate. A proposed "scree test" attenuates this bias, however, and improves accuracy.