Hierarchical and k-means clustering methods work well when clusters are well separated, but when clusters overlap, assigning each point to one cluster is problematic. In the overlap areas, there are points from several clusters sharing the same space. It is especially important to use normal mixtures rather than k-means clustering if you want an accurate estimate of the total population in each group, because it is based on membership probabilities, rather than arbitrary cluster assignments based on borders.
Normal Mixtures Control Panel
For an example of Normal Mixtures, open the Iris.jmp sample data table. This data set was first introduced by Fisher (1936), and includes four different measurements: sepal length, sepal width, petal length, and petal width, performed on samples of 50 each for three species of iris.
On the Cluster launch dialog, assign all four variables to the Y, Columns role, select KMeans from Method menu, and click OK. Select Normal Mixtures from the Method menu, specify 3 for the Number of Clusters, and click Go. The report is shown in Normal Mixtures Report.
Normal Mixtures Report
The Cluster Comparison report gives fit statistics to compare different numbers of clusters. For KMeans Clustering and Self Organizing Maps, the fit statistic is CCC (Cubic Clustering Criterion). For Normal Mixtures, the fit statistic is BIC or AICc. Robust Normal Mixtures does not provide a fit statistic.
Robust Normal Mixtures Control Panel