A Comparison of Two Approaches to Beta-Flexible Clustering.

We introduce a UPGMA based counterpart to the Lance and Williams (1966) p-flexible clustering strategy. This new method is compared with the original p-flexible technique based on WPGMA for a range of fl values from -0.8 to +0.1. Recovery of the known cluster structure from simulated data was evaluated using the Hubert and Arabie (1985) version of the Rand statistic. The algorithm used to generate the simulated clusters in the study included error-free data as well as three other error conditions. The simulated data also varied the number of clusters, the underlying dimensionality, and the density distribution of points to the clusters. Results showed that the flexible UPGMA gives the best recovery for all generated data configurations. Further, the flexible UPGMA method with a small negative β value performed better than the standard UPGMA method where β is set equal to zero. The flexible UPGMA strategy, employed with a narrow β range, is recommended based upon its ability to recover cluster structure over all error conditions.