Given measurements on p variables for each of n individuals, aspects of the problem of clustering the individuals are considered. Special attention is given to models based upon mixtures of distributions, esp. multivariate normal distributions. The relationship between the orientation(s) of the clusters and the nature of the within-cluster covariance matrices is reviewed, as is the inadequacy of transformation to principal components based on the overall (total) covariance matrix of the whole (mixed) sample.

The nature of certain iterative algorithms is elucidated; variations which result from allowing different covariance matrices within clusters are studied.

Key words and phrases: Cluster analysis, Mahalanobis distance, mixture model, isodata, k-means