A probabilistic method for grouping data

A probabilistic method for grouping data has been developed to incorporate measurement error into standard cluster analysis procedures. In the analysis, the data are perturbed using Monte Carlo techniques to simulate the experimental error, and the resultant data sets are clustered. By varying the number of clusters, a procedure is given to estimate the unknown number of groups. This technique and other standard procedures for determining the number of groups are described and compared for three different examples. The probabilistic method is shown to have advantages for determining the number of groups and the probabilities for a sample's membership in the hypothesized groups.