Generation of Random Clusters with Specified Degree of Separation

We propose a random cluster generation algorithm that has the desired features: (1) the population degree of separation between clusters and the nearest neighboring clusters can be set to a specified value, based on a separation index; (2) no constraint is imposed on the isolation among clusters in each dimension; (3) the covariance matrices correspond to different shapes, diameters and orientations; (4) the full cluster structures generally could not be detected simply from pair-wise scatterplots of variables; (5) noisy variables and outliers can be imposed to make the cluster structures harder to be recovered. This algorithm is an improvement on the method used in Milligan (1985).