Exploratory tools for clustering multivariate data

The forward search provides a series of robust parameter estimates based on increasing numbers of observations. The resulting series of robust Mahalanobis distances is used to cluster multivariate normal data. The method depends on envelopes of the distribution of the test statistics in forward plots. These envelopes can be found by simulation; flexible polynomial approximations to the envelopes are given. New graphical tools provide methods not only of detecting clusters but also of determining their membership. Comparisons are made with mclust and k -means clustering.